Two men running
Adam and Bob have exact speeds for walking and running – neither Adam outwalks Bob, nor Bob outruns Adam.
But for a given distance, Adam runs half the time, then walks another half. Bob runs half the distance, then walks another half.
If they were to compete, which distance would Adam win at, and which distances would Bob be the winner at?
Answer:
via Two men running | TechInterviews.
Tags: Interview, puzzles, questions
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on Monday, May 18th, 2009 at 8:21 pm and is filed under Interview, Question, Tech, puzzles.
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Let running speed = r, walking speed = w
total distance x = x1 + x2
total time T = t1 + t2
for Adam:
t = T/2
x1 = rT/2
x2 = wT/2
xa = T * (w+r)/2 ——–1
for Bob:
t1 = x/2r
t2 = x/2w
T = t1 + t2
xb = T * 2rw/(w+r) ——–2
divide 1 by 2 ->
xa/xb = (w^2 + 2wr + r^2) / 4wr ;r > w > 0
Hance, xa/xb is always > 1
so Adam always wins!
Alternate solution: (by another user on source site)
simpler question is… can Adam cover more than 1/2 of distance in 1/2 of the time… if true, Adam always win… since both of them walk for the rest
We know running is faster than walking… so to cover 1/2 of distance by running and walking… running takes less time… therefore it will take less than 1/2 of the time
Now you let Adam run for 1/2 of the time, it will surpass 1/2 the distance
So Adam always win