Motion Problems 2

A man bikes from A toB at 20 km/h. He returnsby car at 60 km/h. The

bike trip is 2 hours longer than the car trip. How far is it from A to B?

Which one?

R X T = DMethod

Bike

Car

20

60

x + 2

x

The distance is alwaysfilled in by multiplyingthe rate and time.

20(x + 2)

60x

Distancesare equal.

20x+40 = 60x20(x+2) = 60x

-20x -20x40 = 40x40 401 = x

A man bikes from A toB at 20 km/h. He returnsby car at 60 km/h. The

bike trip is 2 hours longer than the car trip. How far is it from A to B?

R X T = DMethod

Bike

Car

20

60

x + 2

x

20(x + 2)

60x

What does x represent?What represents distance?

If x=1, distance is:

60x=6060x=??20(x+2)=??

20(x+2)=60

The answer is:

60 km

Problem #2 on Worksheet 61

Vince bikes for 2 hoursat 18 km/h. Then he

rides by car for 3 hours.His total distance is 246 km. How fastdoes the car travel?

Which one?

None of those. It’s this one:

The distances add up to the total distance.

R X T = DMethod

Bike

Car

18

x

23

The distance is alwaysfilled in by multiplyingthe rate and time.

36

3x

246

36+3x = 246-36

3x = 2103 3

x=70

-36

R X T = DMethod

Bike

Car

18

x

23

36

3x

246

What does x represent?

Vince bikes for 2 hoursat 18 km/h. Then he

rides by car for 3 hours.His total distance is 246 km. How fastdoes the car travel?

The answer is:

70 km/h

Problem #3 on Worksheet 61

Cindy bikes from A to B at 20 km/h. She returns by car at 80 km/h. The

bike trip is 3 hours longerthan the car trip. How far

is it from A to B?

Which one?

R X T = DMethod

Bike

Car

20

80

x+3x

The distance is alwaysfilled in by multiplyingthe rate and time.

20(x+3)

80x

Distancesare equal.

20(x+3) = 80x

-20x 60 = 60x

60 601=x

20x+60 = 80x-20x

R X T = DMethod

Bike

Car

20

80

x+3x

20(x+3)

80x

What does x represent?

Cindy bikes from A to B at 20 km/h. She returns by car at 80 km/h. The

bike trip is 3 hours longerthan the car trip. How far

is it from A to B?

The answer is:

80x=

80(1)=80 km

Problem #4 on Worksheet 61

Judy can bike 2 km/h faster than Linda. They travel in

opposite directions for 2 hours. They are then

68 km apart. How fast is each girl traveling?

Which one?

R X T = DPerson

Judy

Linda

x+2

x

22

The distance is alwaysfilled in by multiplyingthe rate and time.

2(x+2)

2x68

2(x+2)+2x = 68

-4

2x+4+2x = 68

4x= 64

4x+4 = 68-4

4 4x=16

R X T = DPerson

Judy

Linda

x+2

x

22

2(x+2)

2x68

What does x represent?

x+2=Judy’s rate of speed

x+2=

x= 16 km/h

18 km/h

x=Linda’s rate of speed

THEEND