Bunuel wrote:

A bicyclist travels uphill from town A to town B for 2 hours at an average speed of 4 miles per hour and returns along the same road at an average speed of 6 miles per hour. What is the bicyclist’s average speed for the round trip, in miles per hour?

(A) 24/5

(B) 5

(C) 26/5

(D) 27/5

(E) 28/5

Average speed = \(\frac{TotalDistance}{TotalTime}\)

(1) Distance between A and B

From Leg 1, \(D=r*t\)

\(D=(4mph*2hrs)=8\) miles

(2) Time, \(t_2\), taken for Leg 2 at 6 mph? D = 8

\((t_2*6)=8\) miles

\(t_2=\frac{8}{6}=\frac{4}{3}\) hours

(3) Average speedTotal distance: \((8 + 8) = 16\) miles

Total time: \((2+\frac{4}{3})=(\frac{6}{3}+\frac{4}{3})=\frac{10}{3}\) hours

Average speed: \(\frac{16}{(\frac{10}{3})}=(16*\frac{3}{10})=\frac{24}{5}\) mph

Answer A

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