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Rate-Time-Distance Problems

- Algebra 1

(No Transcript)

Rate-Time-Distance Problems

- An object is in uniform motion when it moves

without changing its speed, or rate. These

problems fall into 3 categories Motion in

opposite directions, Motion in the same

direction, Round Trip. Each is solved using a

chart, a sketch, and the distance formula.

Sunday, 28 November 2004

Time Speed and Distance

These quantities and found by using these

formulae (rules) Distance Time X Speed

Speed Distance Time Time Distance

Speed

Distance Time X Speed Speed Distance

Time Time Distance Speed

D

S

T

- A car travels at 30 mph for 2 hours. How far has

it travelled? D S x T ? D 30 X 2 ? D 60

miles - A cyclist travels 45 miles in 3 hours. What is

the cyclists speed? S D T ? S 45 3 ? S

15 mph - A plane covers a distance of 1200 miles at a

speed of 300 mph. How long will it take to

complete this journey? - T D S ? T 1200 300 ?

T 4 hours

If the time is in hours and minutes, change it to

hours and decimal parts of a hour like this 2

hours 24 minutes 2. 4

24 60 0.4

Motion in the Same Direction

A helicopter leaves Central Airport and flies

north at 180 mi/h. Twenty minutes later a plane

leaves the airport and follows the helicopter at

330 mi/h. How long does it take the plane to

overtake the helicopter.

t ?

180

180(t ?)

330

t

330t

180

t ?

180(t ?)

330

t

330t

When the plane overtakes the helicopter, the two

distances are equal.

Officer Barbrady left his home at 215 PM and had

driven 60 miles when he ran out of gas. He

walked 2 miles to a gas station, where he arrived

at 415 pm. If he drives 10 times as faster than

he walks, how fast does he walk?

60

10r

r

2

Set to Equal

Office Barbrady walked at a rate of 4/mph

Two cyclists are traveling in the same direction

on the same bike path. One travels at 10mph and

other at 12mph. After how many hours will they be

ten miles apart?

Wondering how to do that?

Step One

DRAW A PICTURE

Two cyclists are traveling in the same direction

on the same bike path. One travels at 10mph and

other at 12mph. After how many hours will they be

ten miles apart?

KEY

10miles

First cyclist (10mph)

Second cyclist (12mph)

Step Two

Make A Chart

Rate

Time

Distance

THE DISTANCE How far they or it has traveled.

THE DISTANCE is equal to THE RATE times THE

TIME.

THE RATE How fast they or it is traveling at.

Rate

Time

Distance

THE TIME How long it takes to go THE DISTANCE.

Since you are trying to figure out what the time

is it is X

Step Three

SET THE EQUATION TO EQUAL

Going back to the picture.

The first cyclist plus ten miles is

equal to

the second cyclist

10miles

First cyclist (10mph)

Second cyclist (12mph)

Step Four

SOLVE THE EQUATION

10X 10 12X

First Cyclist

Second Cyclist

Distance (miles) apart from the two cyclist

Step Four cont...........

10X 10 12X

10X

10X

I

I

10 2X

I

I

2

2

5 X

Step Five

COMPLETING THE CHART

Rate

Time

Distance

X

5

10x

50

12x

60

X

5

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- Two cars leave the same town at the same time.

One travels north at 60 mph and the other south

at 45 mph. In how many hours will they be 420

miles apart?

t

Car 1

60

60t

t

45t

Car 2

45

Car 1

60

t

60t

45

t

45t

Car 2

In 4 hours the cars will be 420 miles apart.

Motion R T D

- Two cars leave the same town at the same time.

One travels north at 60 mph and the other south

at 45 mph. - In how many hours will they be 420 miles apart?
- R T D
- 1st car (60 mph) (time) distance
- 2nd car (45 mph) (time) distance

Motion R T D

- Two cars leave the same town at the same time.

One travels north at 60 mph and the other south

at 45 mph. - In how many hours will they be 420 miles apart?
- R T D
- 1st car (60 mph) (time) distance
- 2nd car (45 mph) (time) distance
- Let t time
- Distance apart 420 60t 45t

Motion R T D

- Two cars leave the same town at the same time.

One travels north at 60 mph and the other south

at 45 mph. - In how many hours will they be 420 miles apart?
- 1st car 60 mph time (t) distance
- 2nd car 45 mph time (t) distance
- Distance apart 420 60t 45t
- 105t 420
- t 4 hours

Check

- Motion R T D
- Two cars leave the same town at the same time.

One travels north at 60 mph and the other south

at 45 mph. - In how many hours will they be 420 miles apart?
- CHECK t 4 hours
- 60 4 45 4 420 ??
- 240 180 420 OK
- They will be 420 miles apart in 4 hours.

Bicyclist Brent and Jane started at noon from 60

km apart and rode toward each other, meeting at

130 P.M. Brents speed was 4 km/h greater than

Janes speed. Find their speeds.

r 4

1.5

1.5(r 4)

r

1.5

1.5r

r 4

1.5(r 4)

1.5

1.5

1.5r

r

Round Trip

A ski lift carried Maria up a slope at the rate

of 6 km/h, and she skied back down parallel to

the lift at 34 km/h. The round trip took 30 min.

How far did she ski?

6

0.5 - t

6(0.5 t)

34

t

34 t

Maria skied for 0.075h, or 4.5 min, for a

distance of 2.55km.

6

0.5 - t

6(0.5 t)

34

t

34 t

In round trip problems, the two distances are

equal.

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Another fine lesson

Given by the great teacher

Mr. Stubbs

THE END

Rate-Time-Distance Problems

- Review Additional Problems Part B

Sherry and Bob like to jog in the park. Sherry

can jog at 5 mph, while Bob can jog at 7 mph. If

Sherry starts 30 minutes ahead of Bob, how long

will it take Bob to catch up to Sherry?

Let x the time it takes Bob to catch Sherry

x 1/2

5(x 1/2)

5

7

x

7x

Sherry started 30 minutes or 1/2 hour before

Bob, so her time must reflect that amount. Rate

is in miles per hour, time must be in hours so

our units match.

x 1/2

5(x 1/2)

5

7

x

7x

When Bob catches-up with Sherry their distances

will be equal. So the Equation will be sherrys

distance equals Bobs distance.

It will take Bob 1.25 hrs to catch up with Sherry.

Bernadette drove 120 miles. The first part of the

trip she averaged 60 mph, but on the second part

of the trip she ran into some congestion and

averaged 48 mph. If the total driving time was

2.2 hours, how much time did she spend at 60 mph?

60

60t

t

48

2.2-t

48(2.2-t)

60

t

60t

2.2-t

48

48(2.2-t)

The time traveled at 60 mph was 1.2 hours.

A passenger trains speed is 60 mi/h, and a

freight trains speed is 40 mi/h. The passenger

train travels the same distance in 1.5 h less

time than the freight train. How long does each

train take to make the trip.

Freight train 4.5h. Passenger train 3h

Ali rode her bike to visit a friend. She

traveled at 10 mi/h. While she was there, it

began to rain. Her friend drove her home in a

car traveling 25 mi/h. Ali took 1.5 hours longer

to go to her friends than to return home. How

many hours did it take Ali ti ride to her

friends house?

2.5 h

Katie rides her bike the same distance as Jill

walks. Katie rides her bike 10 km/h faster than

Jill walks. If it takes Katie 1 h. and Jill 3 h

to travel the same distance, how fast does each

travel?

Katie 15 km/ h Jill 5 km/h

At 1000 A.M., a car leaves a house at a rate of

60 mi/h. At the same time, another car leaves

the same house at a rate of 50 mi/h in the

opposite direction. At what time will the car be

330 miles apart?

100 P.M.

Brittney begins walking ay 3 mi/h toward the

library. Her friend meets her at the halfway

point and drives her the rest of the way to the

library. The distance to the library is 4 miles.

How many hours did Marla walk?

2/3 h or 40 min.

Ryan begins walking towards Johns house at 3

mi/h. John leaves his house at the same time and

walks towards Freds house on the same path at a

rate of 2 mi/h. How long will it be before they

meet if the distance between the houses is 4

miles?

4/5 h. or 48 min

A train leaves the station at 600 P.M. traveling

west at 80 mi/h. On a parallel track, a second

train leaves the station 3 hours later traveling

west at 100 mi/h. At what time will the second

train catch up with the first?

900 A.M.

It takes 1 hour longer to fly to St. Paul at 200

mi/h than it does to return at 250 mi/h. How far

way is St. Paul.

1000 mi

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Motion problems use the equation D RT where D

is the distance traveled, R is the rate when

traveling and T is the time spent traveling.

It is helpful to use a D RT grid when

solving motion problems as shown in the following

example.

- Juan and Amal leave DC at the same time headed

south on I-95. If Juan averages 60 mph and Amal

averages 72 mph how long will it take them to be

30 miles apart? - (Now would be a good time for a guess. Write

yours down and try it in this table.)

We are looking for a time where Juan and Amal

will be 30 miles apart. How do we represent the

distance between the two men?

60x - 72x

Or is it 72x - 60x. Which of these two would be

positive?

The correct equation is 72x - 60 x 30

- The purpose of the grid is to find an algebraic

name for each distance. Notice that the distance

30 miles does not appear in the grid because

neither Juan nor Amal traveled 30 miles. Notice

also that we could use x for each time since Juan

and Amal were on the road for the same amount of

time. We will need to work 30 miles into the

equation as follows - 72x 60x 30

12x 30 - x 2.5 hrs.

Practice Problems Motion 1. Tonya and Freda

drive away from Norfolk on the same road in the

same direction. If Tonya is averaging 52 mph and

Freda is averaging 65 mph, how long will it take

for them to be 39 miles apart? 2. Tonya and

Freda drive away from Norfolk on the same road in

opposite directions. If Tonya is averaging 52 mph

and Freda is averaging 65 mph, how long will it

take for them to be 39 miles apart? Round your

answer to the nearest minute.

For worked out solutions click to next slide.

1. Tonya and Freda drive away from Norfolk on

the same road in the same direction. If Tonya is

averaging 52 mph and Freda is averaging 65 mph,

how long will it take for them to be 39 miles

apart? Let x time it takes for them to be 39

miles apart. Construct a table to put your

information in.

Tonya and Freda drive away from Norfolk on the

same road in the same direction. If Tonya is

averaging 52 mph and Freda is averaging 65 mph,

how long will it take for them to be 39 miles

apart?

We let x stand for the time they have been

driving which would be the same in this case.

How far they have gone (distance) is written in

the chart by using the known information and the

formula RTD

Tonya and Freda drive away from Norfolk on the

same road in the same direction. If Tonya is

averaging 52 mph and Freda is averaging 65 mph,

how long will it take for them to be 39 miles

apart?

Tonya and Freda are headed in the same direction

so we can picture their distances as this

52x

Tonya

39 mi

65x

Freda

Do you see the equation forming from our picture?

Tonya and Freda drive away from Norfolk on the

same road in the same direction. If Tonya is

averaging 52 mph and Freda is averaging 65 mph,

how long will it take for them to be 39 miles

apart?

52x

Tonya

39 mi

65x

Freda

One way to look at it might be to say 52x 39

65x Or another way might be to say 65x 52x

39 Both are correct and will give you the correct

answer of 3 hrs.

2. Tonya and Freda drive away from Norfolk on the

same road in opposite directions. If Tonya is

averaging 52 mph and Freda is averaging 65 mph,

how long will it take for them to be 39 miles

apart? Round your answer to the nearest minute.

Now they are going in opposite directions, but we

will begin the same way by constructing our table.

Tonya and Freda drive away from Norfolk on the

same road in opposite directions. If Tonya is

averaging 52 mph and Freda is averaging 65 mph,

how long will it take for them to be 39 miles

apart? Round your answer to the nearest minute.

As you can see the table is the same, so only the

picture of the event must change. Now it looks

like this

START

52x

65x

Freda

Tonya

39 miles

Do you see the equation forming from this picture?

Tonya and Freda drive away from Norfolk on the

same road in opposite directions. If Tonya is

averaging 52 mph and Freda is averaging 65 mph,

how long will it take for them to be 39 miles

apart? Round your answer to the nearest minute.

START

52x

65x

Tonya

39 miles

Freda

52x 65x 39 117x39 X 1/3 of an hour or 1/3

of 60 min 20 minutes

3. Bernadette drove 120 miles. The first part of

the trip she averaged 60 mph, but on the second

part of the trip she ran into some congestion and

averaged 48 mph. If the total driving time was

2.2 hours, how much time did she spend at 60 mph?

The question here deals with time. Again,

lets Fill in the chart.

Bernadette drove 120 miles. The first part of the

trip she averaged 60 mph, but on the second part

of the trip she ran into some congestion and

averaged 48 mph. If the total driving time was

2.2 hours, how much time did she spend at 60 mph?

t

60t

2.2 - t

48(2.2 t)

This time totals are given for both time traveled

and distance traveled. Thus totals dont belong

in the chart. Bernadette did not travel 2.2

hours at 60 mph nor did she travel 2.2 hours at

48 mph. She traveled 2.2 hours total at both of

those speeds. So how do we write this in the

chart. Click to observe.

Distance is again computed by formula RT D

Bernadette drove 120 miles. The first part of the

trip she averaged 60 mph, but on the second part

of the trip she ran into some congestion and

averaged 48 mph. If the total driving time was

2.2 hours, how much time did she spend at 60 mph?

t

60t

2.2 - t

48(2.2 t)

What is the picture for this problem?

60t

48(2.2 t)

Dist 1st leg Dist 2nd leg

Total dist. 120 miles

Do you see the equation from the picture?

60t 48(2.2 t) 120

Bernadette drove 120 miles. The first part of the

trip she averaged 60 mph, but on the second part

of the trip she ran into some congestion and

averaged 48 mph. If the total driving time was

2.2 hours, how much time did she spend at 60 mph?

60t

48(2.2 t)

Dist 1st leg Dist 2nd leg

Total dist. 120 miles

60t 48(2.2 t) 120 60t 105.6 48t

120 12t 14.4 t 1.2 hours at 60mph

4. Dr. John left New Orleans at 12 noon. His

drummer left at 100 traveling 9 mph faster. If

the drummer passed Dr. John at 600, what was the

average speed of each?

Now we dont know the speed. We do know

something about time. Lets see how we can fill

in the chart.

Dr. John left New Orleans at 12 noon. His drummer

left at 100 traveling 9 mph faster. If the

drummer passed Dr. John at 600, what was the

average speed of each?

6x

6

5

5(x 9)

The problem is over when the drummer passes Dr.

John at 6 PM, so how long has Dr. John been

driving?

How long has the drummer been driving?

What is our picture?

6x

Dr. John

5x 45

Drummer

Drummer passing Dr. John

Dr. John left New Orleans at 12 noon. His drummer

left at 100 traveling 9 mph faster. If the

drummer passed Dr. John at 600, what was the

average speed of each?

6

5

Dr. John

Drummer

What equation does the picture suggest?

The two distances are equal thus 6x 5(x

9) 6x 5x 45 X 45 mph for Dr. John X 9

54 mph for the drummer

Car and Bus

- Motion R T D
- When Michael drives his car to work, the trip

takes ½ hour. When he rides the bus, it takes

¾ hour. The average speed of the bus is 12 mph

less than his speed when driving. - Find the distance he travels to work.

Car and Bus

- Motion R T D
- When Michael drives his car to work, the trip

takes ½ hour. When he rides the bus, it takes

¾ hour. The average speed of the bus is 12 mph

less than his speed when driving. - Find the distance he travels to work.
- Let D distance to work

Car and Bus

- Motion R T D
- When Michael drives his car to work, the trip

takes ½ hour. When he rides the bus, it takes

¾ hour. The average speed of the bus is 12 mph

less than his speed when driving. - Find the distance he travels to work.
- Let D distance to work
- R D/T

Car and Bus

- Motion R T D
- When Michael drives his car to work, the trip

takes ½ hour. When he rides the bus, it takes

¾ hour. The average speed of the bus is 12 mph

less than his speed when driving. - Find the distance he travels to work.
- Let D distance to work
- R D/T R(car) D / (½)
- R(bus) D / (¾)
- Equation?

Car and Bus

- Motion R T D
- When Michael drives his car to work, the trip

takes ½ hour. When he rides the bus, it takes

¾ hour. The average speed of the bus is 12 mph

less than his speed when driving. - Find the distance he travels to work.
- Let D distance to work
- R D/T R(car) D / (½) 2D
- R(bus) D / (¾) 4D/3
- Equation

Car and Bus

- Motion R T D
- When Michael drives his car to work, the trip

takes ½ hour. When he rides the bus, it takes

¾ hour. The average speed of the bus is 12 mph

less than his speed when driving. - Find the distance he travels to work.
- Let D distance to work
- R D/T R(car) D / (½) 2D
- R(bus) D / (¾) 4D/3
- Equation

Check

- Motion R T D
- When Michael drives his car to work, the trip

takes ½ hour. When he rides the bus, it takes

¾ hour. The average speed of the bus is 12 mph

less than his speed when driving. - Find the distance he travels to work.
- Check D18
- The distance to work is 18 miles.

(Rate)(Time) Distance

- A truck driver delivered a load to Richmond from

Washington, D.C., averaging 50 mph for the trip.

He picked up another load in Richmond and

delivered it to NYC, averaging 55 mph on this

part of the trip. The distance from Richmond to

NYC is 120 miles more than the distance from

Washington to Richmond. If the entire trip

required a driving time of 6 hours, find the

distance from Washington to Richmond.

Rate Time Distance

- A truck driver delivered a load to Richmond from

Washington, D.C., averaging 50 mph for the trip.

He picked up another load in Richmond and

delivered it to NYC, averaging 55 mph on this

part of the trip. The distance from Richmond to

NYC is 120 miles more than the distance from

Washington to Richmond. If the entire trip

required a driving time of 6 hours, find the

distance from Washington to Richmond. - Let x distance Washington to Richmond

Rate x Time Distance

- A truck driver delivered a load to Richmond from

Washington, D.C., averaging 50 mph for the trip.

He picked up another load in Richmond and

delivered it to NYC, averaging 55 mph on this

part of the trip. The distance from Richmond to

NYC is 120 miles more than the distance from

Washington to Richmond. If the entire trip

required a driving time of 6 hours, find the

distance from Washington to Richmond. - Let x distance Washington to Richmond
- Rate Time Distance
- W-R 50
- R-NYC 55

Rate x Time Distance

- A truck driver delivered a load to Richmond from

Washington, D.C., averaging 50 mph for the trip.

He picked up another load in Richmond and

delivered it to NYC, averaging 55 mph on this

part of the trip. The distance from Richmond to

NYC is 120 miles more than the distance from

Washington to Richmond. If the entire trip

required a driving time of 6 hours, find the

distance from Washington to Richmond. - Let x distance Washington to Richmond
- Rate Time Distance
- W-R 50 x
- R-NYC 55 x 120

Rate x Time Distance

- A truck driver delivered a load to Richmond from

Washington, D.C., averaging 50 mph for the trip.

He picked up another load in Richmond and

delivered it to NYC, averaging 55 mph on this

part of the trip. The distance from Richmond to

NYC is 120 miles more than the distance from

Washington to Richmond. If the entire trip

required a driving time of 6 hours, find the

distance from Washington to Richmond. - Let x distance Washington to Richmond
- Rate Time Distance
- W-R 50 x
- R-NYC 55 x 120
- 6 hours total

Rate x Time Distance

- A truck driver delivered a load to Richmond from

Washington, D.C., averaging 50 mph for the trip.

He picked up another load in Richmond and

delivered it to NYC, averaging 55 mph on this

part of the trip. The distance from Richmond to

NYC is 120 miles more than the distance from

Washington to Richmond. If the entire trip

required a driving time of 6 hours, find the

distance from Washington to Richmond. - Let x distance Washington to Richmond
- Rate Time Distance
- W-R 50 x/50 x
- R-NYC 55 (x120)/55 x 120
- 6 hours total

Rate x Time Distance

- A truck driver delivered a load to Richmond from

Washington, D.C., averaging 50 mph for the trip.

He picked up another load in Richmond and

delivered it to NYC, averaging 55 mph on this

part of the trip. The distance from Richmond to

NYC is 120 miles more than the distance from

Washington to Richmond. If the entire trip

required a driving time of 6 hours, find the

distance from Washington to Richmond. - Let x distance Washington to Richmond
- Rate Time Distance
- W-R 50 x/50 x
- R-NYC 55 (x120)/55 x 120
- 6 hours total
- x/50 (x120)/55 6

Rate x Time Distance

- A truck driver delivered a load to Richmond from

Washington, D.C., averaging 50 mph for the trip.

He picked up another load in Richmond and

delivered it to NYC, averaging 55 mph on this

part of the trip. The distance from Richmond to

NYC is 120 miles more than the distance from

Washington to Richmond. If the entire trip

required a driving time of 6 hours, find the

distance from Washington to Richmond. - Let x distance Washington to Richmond
- Rate Time Distance
- W-R 50 x/50 x
- R-NYC 55 (x120)/55 x 120
- 6 hours total
- x/50 (x120)/55 6 LCD 550
- 11x 10x 1200 3300

Rate x Time Distance

- A truck driver delivered a load to Richmond from

Washington, D.C., averaging 50 mph for the trip.

He picked up another load in Richmond and

delivered it to NYC, averaging 55 mph on this

part of the trip. The distance from Richmond to

NYC is 120 miles more than the distance from

Washington to Richmond. If the entire trip

required a driving time of 6 hours, find the

distance from Washington to Richmond. - Let x distance Washington to Richmond
- Rate Time Distance
- W-R 50 x/50 x
- R-NYC 55 (x120)/55 x 120
- 6 hours total
- x/50 (x120)/55 6 LCD 550
- 11x 10x 1200 3300
- 21x 2100
- x 100 CHECK

Uniform Motion - Trucks

Michele drove her empty rig 300 miles to Salina

to pick up a load of cattle. When the rig was

finally loaded, her average speed was 10 mph less

than when the rig was empty. If the return trip

took her 1 hour longer , then what was her

average speed with the rig empty?

6-9

Page 374 (Figure 6.1)

Uniform Motion - Trucks

Michele drove her empty rig 300 miles to Salina

to pick up a load of cattle. When the rig was

finally loaded, her average speed was 10 mph less

than when the rig was empty. If the return trip

took her 1 hour longer , then what was her

average speed with the rig empty? x average

empty speed

6-9

Page 374 (Figure 6.1)

Uniform Motion - Trucks

Michele drove her empty rig 300 miles to Salina

to pick up a load of cattle. When the rig was

finally loaded, her average speed was 10 mph less

than when the rig was empty. If the return trip

took her 1 hour longer , then what was her

average speed with the rig empty? x average

empty speed Rate Time Distance To

Salina Return

6-9

Page 374 (Figure 6.1)

Uniform Motion - Trucks

Michele drove her empty rig 300 miles to Salina

to pick up a load of cattle. When the rig was

finally loaded, her average speed was 10 mph less

than when the rig was empty. If the return trip

took her 1 hour longer , then what was her

average speed with the rig empty? x average

empty speed Rate Time Distance To

Salina 300 Return 300

6-9

Page 374 (Figure 6.1)

Uniform Motion - Trucks

Michele drove her empty rig 300 miles to Salina

to pick up a load of cattle. When the rig was

finally loaded, her average speed was 10 mph less

than when the rig was empty. If the return trip

took her 1 hour longer , then what was her

average speed with the rig empty? x average

empty speed Rate Time Distance To Salina x

300 Return x - 10 300

6-9

Page 374 (Figure 6.1)

Uniform Motion - Trucks

Michele drove her empty rig 300 miles to Salina

to pick up a load of cattle. When the rig was

finally loaded, her average speed was 10 mph less

than when the rig was empty. If the return trip

took her 1 hour longer , then what was her

average speed with the rig empty? x average

empty speed Rate Time Distance To Salina x

300/x 300 Return x - 10 300/(x - 10)

300 300/x 1 300/(x - 10)

6-9

Page 374 (Figure 6.1)

Uniform Motion - Trucks

Michele drove her empty rig 300 miles to Salina

to pick up a load of cattle. When the rig was

finally loaded, her average speed was 10 mph less

than when the rig was empty. If the return trip

took her 1 hour longer , then what was her

average speed with the rig empty? x average

empty speed Rate Time Distance To Salina x

300/x 300 Return x - 10 300/(x - 10)

300 300/x 1 300/(x - 10) LCD x (x -

10) 300 (x - 10) x (x - 10) 300 x

6-9

Page 374 (Figure 6.1)

Uniform Motion - Trucks

Michele drove her empty rig 300 miles to Salina

to pick up a load of cattle. When the rig was

finally loaded, her average speed was 10 mph less

than when the rig was empty. If the return trip

took her 1 hour longer , then what was her

average speed with the rig empty? x average

empty speed Rate Time Distance To Salina x

300/x 300 Return x - 10 300/(x - 10)

300 300/x 1 300/(x - 10) LCD x (x -

10) 300 (x - 10) x (x - 10) 300 x 300 x

- 3000) x2 10 x 300 x x2 10 x 3000

0

6-9

Page 374 (Figure 6.1)

Uniform Motion - Trucks

Michele drove her empty rig 300 miles to Salina

to pick up a load of cattle. When the rig was

finally loaded, her average speed was 10 mph less

than when the rig was empty. If the return trip

took her 1 hour longer , then what was her

average speed with the rig empty? x average

empty speed Rate Time Distance To Salina x

300/x 300 Return x - 10 300/(x - 10)

300 300/x 1 300/(x - 10) LCD x (x -

10) 300 (x - 10) x (x - 10) 300 x 300 x

- 3000) x2 10 x 300 x x2 10 x 3000

0 (x - 60) (x 50) 0

6-9

Page 374 (Figure 6.1)

Uniform Motion - Trucks

Michele drove her empty rig 300 miles to Salina

to pick up a load of cattle. When the rig was

finally loaded, her average speed was 10 mph less

than when the rig was empty. If the return trip

took her 1 hour longer , then what was her

average speed with the rig empty? x average

empty speed Rate Time Distance To Salina x

300/x 300 Return x - 10 300/(x - 10)

300 300/x 1 300/(x - 10) LCD x (x -

10) 300 (x - 10) x (x - 10) 300 x 300 x

- 3000) x2 10 x 300 x x2 10 x 3000

0 (x - 60) (x 50) 0 x 60 x -

50 CHECK Not Possible

6-9

Page 374 (Figure 6.1)

Uniform Motion

- Driving to Florida
- Susan drove 1500 miles to Daytona Beach for

spring break. On the way back she averaged 10

mph less, and the drive back took 5 hours longer.

Find Susans average speed on the way to Daytona

Beach.

Driving to Florida

6-10

Page 355 (Figure 6.1)

Driving to Florida

- Susan drove 1500 miles to Daytona Beach for

spring break. On the way back she averaged 10

mph less, and the drive back took 5 hours longer.

Find Susans average speed on the way to Daytona

Beach. - Let x average speed going
- x - 10 average speed returning
- R T D
- Going x 1500
- Returning x 10 1500

The Problem

- Two trains leave Houston at the same time, one

traveling east, the other west. The first train

traveled at 50 mph and the second at 40 mph. In

how many hours will the trains be 405 miles apart?

Table

- Rate of Train 1 50 mph

- Rate of Train 2 40 mph

- Time for both trains t

50 mph

t

50t

40 mph

- Total for train 1 50t

40t

t

- Total for train 2 40 t

- Rate x time distance

The Math

- Set trains totals to equal 405 miles

This is our equation

50t40t405miles

- Add both totals

40t 50t 90t

- Divide both sides by 90

90t 405miles 90 90

- T 4.5 hours

T4.5hours

Our Answer

It will take 4.5 hours for the trains to be 405

miles apart!

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