Bunuel wrote:
Warren and Rubin race around an oval track. Warren runs at a uniform rate of one lap every 7 minutes, and Rubin runs at a uniform rate of one lap every 5 minutes. If they both start at the same time. How many minutes will it take for Rubin to get exactly one lap ahead of Warren.
(A) 12
(B) 13 1/2
(C) 15
(D) 16.7
(E) 17.5
Rate of Warren = \(\frac{1}{7}\) lap/minute
Say, distance travelled by Warren = d laps
So, time taken by Warren = \(\frac{d}{1/7}\) = 7d
Rate of Rubin = \(\frac{1}{5}\) lap/minute
Distance travelled by Rubin = d+1 laps
Time taken = \(\frac{(d + 1)}{(1/5)}\) = 5d + 5
Now we can equate their times as both ran for equal duration
7d = 5d + 5
d =\(\frac{5}{2}\)
Minutes will it take for Rubin to get exactly one lap ahead of Warren = 5d + 5
\(5 * \frac{5}{2} + 5\)
\(\frac{25}{2} + 5\)
17.5 (E)
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