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Solution to CyberTeaser B309

It took Nick 3 hours 12 minutes -- that is, 16/5 hours -- to reach Georgetown, and it took George 2 hours 40 minutes -- that is, 8/3 hours -- to reach Nicktown. Denoting the distance between the towns by L miles, we find that Nick was walking at a speed of 5L/16 mph and George's speed was 3L/8 mph. We can determine the length of the bridge l, since we know that George crossed it one minute faster than Nick: 16l/5L - 8l/3L = 1/60. This yields l = L/32. Let t be the moment the boys reached the bridge. At this moment, the total distance walked by both boys was L - L/32 = 31L/32. On the other hand, this equals the sum of the distances walked by each of them -- that is,

(5L/16)[t - (10 + 3/10)] + (3L/8)(t - 9) = (L/16)(11t - 211/2).

Setting these expressions equal to each other, we obtain

(L/16)(11t - 211/2) = 31L/32,

which gives us t = 11 o'clock.

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