Warren runs at a rate of 1 lap every 7 mins
Rubin runs at a rate of 1 lap every 5 mins
In 7 mins , Rubin must have completed 2/5th of an additional lap by the time Warren completes Warren's first lap.
Time taken for Rubin to get exactly one lap ahead of Warren = 5/2 * 7 mins = 17.5 mins

Answer E
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I plugged in the values.

by the the time Rubin completed 3 laps in 15 minutes , Warren completed only 15/7 ~2.1 of the lap

plug in 17.5 and we get 17.5/5 = 3.5 rounds for Rubin and 17.5/7 = 2.5 Rounds for for warren
The difference is thus 1 round so :E 17.5 is the answer

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

W runs 1/7, or 5/35, laps per minute
R runs 1/5, or 7/35, laps per minute
R gains 2/35 laps per minute on W
1 lap/(2/35) laps per minute=17.5 minutes
E

Warren runs one lap in 7 mins
Rubin runs one lap in 5 mins

We can say in 7 mins Warren completes 1 lap while Rubin complete 1+2/5th of the second lap.
in the next 7 mins warren completes to laps while Rubin completes 1+1+ 2/5+2/5 (4/5 lap ahead of warren)

to complete 1/5th of lap Rubin will require 3.5 mins.

Total time required by Rubin to be ahead of Warren by exactly one lap = 7 + 7 + 3.5 = 17.5 mins

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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