Posted: 3/10/2004 6:55:17 PM EDT
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First one to get this one and show their work wins 200 points and a free guitar pick*! Two guys are swimming laps back and forth across the length of a pool with constant speeds and essentially instantaneous turns at the ends of the pool. Determine the length of the pool if they leave from opposite ends at the same time and meet for the first time 21 meters from one end of the pool, continue their courses, turn around at the ends, and meet again 8 meters from the opposite end of the pool. * Approximate retail value of guitar pick is $0.75, winner responsible for shipping and handling ($435.99). Gribble out |
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Figuring out that they start out from opposite pool ends (One starts from the North side, the other from the South end for any DUmmy’s lurking around), that would be 21 times 2 or 42 meters long. Guesstimate that they are each about 2 meters long and I have… [b]46[/b] meters long. But aren’t “Olympic Size” pools supposed to be 50 meters long? It could have been a couple of long dives into the pool. Send the bill to Rosie. |
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|----- d -----| v1 v2 ---> <--- (d-21)/t1 = v1 (21)/t1 = v2 (2d-8)/t2 = v1 (d+8)/t2 = v2 (d-21)/t1 = (2d-8)/t2 (21)/t1 = (d+8)/t2 [(2d-8)t1]/(d-21) = t2 [(d+8)t1]/21 = t2 (2d-8)/(d-21) = (d+8)/(21) (d+8)(d-21) = (21)(2d-8) (d+8)(d-21) = (21)(2d-8) d^2 - 13d - 168 = 42d - 168 d^2 = 55d d = 55 |