Question

Two children who are bored while waiting for their flight at the airport decide to race from one end of the 20 m-long moving sidewalk to the other and back. Phillippe runs on the sidewalk at 2.0 m/s (relative to the side walk). Renee runs on the floor at 2.0  m/s. The sidewalk moves at 1.5  m/s relative to the floor.Both make the turn instantly with no loss of speed.

Part1
Who wins the race? (Phillippe or Renee?)

Part2
By how much time does the winner win? (2 sig figs and in seconds)

Answer 1

Let's calculate how long it takes each of them to run the wholerace.

Renee: She must travel 20 m to the end of the track and then 20 mback, so a total of 40 m. She runs 2.0 m/s. Distance = speed *time, so time = distance/speed. Thus, her time is 40/2.0 = 20seconds.

Phillippe: When Phillippe is running in the same direction as thesidewalk is moving, his velocity relative to the sidewalk is addedto the velocity of the sidewalk for a total velocity of 2.0 + 1.5 =3.5 m/s relative to the ground. He runs 20 m at this pace, so ittakes him 20/3.5 = 5.7 sec. On the way back, the sidewalk is movingin the opposite direction, so his speed relative to the ground is2.0 - 1.5 = 0.5 m/s. Thus, the time it takes him to run back is20/.5 = 40 sec. So his total time is 40 + 5.7 = 45.7 seconds.

Clearly, Renee wins therace. She wins by a total of 45.7 - 20 = 25.7 seconds. In 2 sigfigs, this is 26seconds.

Edit: Also, I don't know what the etiquette about this is, but theperson who posted below me has absolutely no idea what they'retalking about. They misunderstood the question and also didn't evenget the correct answer for the misinterpreted question...