6th Grade Math Textbook, Fundamentals

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Problem 2:A model car is moving toward a wall at the rate of 6 centimeters
per second (cm/s). At the moment the car is 810 cm from the wall, a fly—which
had been resting on the front of the car—flies directly toward the wall at the
rate of 10 cm/s. When the fly reaches the wall, it immediately reverses direction
until it again reaches the car, at which moment it reverses direction again and
heads for the wall. It continues going back and forth between the car and the
wall until the car hits the wall! (All the while, the fly maintains its 10 cm/s air
speed.) In all, how many centimeters did this fly travel?

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Lesson 9-14 for exercise sets.

Read to understand what is being asked.

List the facts and restate the question.

Facts: The model car moves toward a wall at the rate of 6 cm/s.

When the car is 810 cm from the wall, the fly begins to fly back

and forth between the car and the wall at a speed of 10 cm/s.

The fly continues flying until the car hits the wall.

Question:How far does the fly go in all?

Select a strategy.

Because you know the car’s speed and the fly’s speed, you could determine

where the car was when the fly first reached the wall. You could then record

the initial 810 cm the fly flew, and then you could reset the problem from there.

This could take some time, however. Perhaps a more efficient strategy would

be to Adopt a Different Point of View.

Apply the strategy.

Think about how much timethe fly was flying rather than the distance

it flew. Because it never changed its speed, if you know how long it was

in the air, you can determine how far it traveled. You know the fly was

flying for as long as it took the car to reach the wall. How long was that?

To find how long, use the Distance Formula.

distance rate • time time 

time 135 s

So the fly was flying for 135 seconds.

The fly’s rate was 10 cm/s, so in 135 seconds, it would have flown

10 • 135, or 1350 cm.

distance

rate

810 cm

6 cm/s

Check to make sure your answer makes sense.

Because the fly moved at 10 cm/s, flying 1350 cm would have taken

135 seconds.

Because the car traveled at 6 cm/s, in 135 seconds, it would have

traveled 135 • 6, or 810, cm. This is exactly the car’s distance from

the wall when the fly started flying.

So the answer checks.