Walkway Fast and Furious
A 100 foot long moving walkway moves at a constant rate of 6 feet per second. Ash steps onto the start of the walkway and stands.
Bob steps onto the start of the walkway two seconds later and strolls forward along the walkway at a constant rate of 4 feet per second.
Two seconds after that, Chip reaches the start of the walkway and instead of getting on the walkway, moves briskly forward beside the walkway at a constant rate of 8 feet per second.
At a certain time, one of these three persons is exactly halfway between the other two. At that time, find the distance in feet between the start of the walkway and the middle person.
The answer is 52.
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Clearly we have people moving at speeds of 6,8 and 10 feet/second. Notice that out of the three people, Chip is at the largest disadvantage to begin with and since all speeds are close, it is hardest for him to catch up. Furthermore, Bob is clearly the farthest along. Thus it is reasonable to assume that there is some point when Ash is halfway between Chip and Bob. At this time s, we have that
(8(s-4)+10(s-2)) /{2}=6s After solving, s=26/3. At this time, Ash has traveled 6*{26/3}=52 feet.
We could easily check that Ash is in the middle by trying all three possible cases. {6s + 8(s-4))/2} = 10(s-2) yields that s = 4/3, which can be disregarded since both Bob and Cy hadn't started yet. {6s + 10(s-2)/{2} = 8(s-4) yields that -10=-32, a contradiction. Thus, the answer is 52.