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Sarah and John are running clockwise around a circular track with radius 25 meters. They start at the same position, and Sarah runs at 2.7 m/s while John runs at 2.2 m/s. How far away from their starting point are they when Sarah catches up and passes John for the first time after the start?

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sqdancefan

Answer:

  62.8 m

Step-by-step explanation:

The length of one lap is ...

  C = 2πr = 2π(25 m) = 50π m ≈ 157.08 m

Sarah is gaining ground on John at the rate of 2.7 m/s -2.2 m/s = 0.5 m/s. So it will take Sarah ...

  157.08 m/(0.5 m/s) = 314.16 s

to run 1 lap farther than John does.

It takes Sarah ...

  157.08 m/(2.7 m/s) = 58.18 s

to run 1 lap, so in the time it takes her to catch John, she will have run ...

  314.16 s/(58.18 s/lap) = 5.4 laps

She (and John) will be 0.4 laps from their start when they meet again. That distance is ...

  (0.4)(157.08 m) = 62.8 m

Sarah will catch and pass John 62.8 meters from their starting position.

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