Xavier and Yonette are waiting for their plane at an airport, when Xavier proposes a race:
"See that moving sidewalk? Why don't you run on it, and then when you reach the end turn back and run to where you started from? I meanwhile will run the same path, but right next to it rather than on it."
Yonette thought about it and said:
"But I don't see the point... We both run with the same speed, and it's the same distance. Sure, I will gain a bit on you while the sidewalk increases my speed, but then I will just lose the advantage while I'm running back and we will arrive at the same time."
Assuming Xavier and Yonette do run with the same speed, who will win the race?
(In reply to
Puzzle Answer by K Sengupta)
The walking speed of Xavier
= The walking speed of Yonette
= w (say)
The speed of the sidewalk = s (say)
WLOG, we can assume that the length of the sidewalk is 1 unit.
Then, the average speed of Xavier
= His average walking speed
= w
The average speed of Yonette (walking with sidewalk)
2 2(w^2-s^2) s^2
= ------------------------------- = --------------------------- = w - -----
1/(w+s) + 1/(w-s ) 2w w
Then, for any finitely positive real number s, we must have:
s^2
w > w - ------
w
Since the average speed of Xavier is greater than that of Yonette, and they cover the same distance, it is apparent that Xavier will win the race.
Edited on April 14, 2023, 10:31 pm
Explanation to Puzzle Answer
