Let's assume the distance from home to office be 20 miles, which he takes an hour traveling in the taxi at

20(r) miles/hrWhile going to the office, he takes 2 hours walking at

5(p) miles/hr, and the rest of the distance in 1 hour cycling at

10(q) miles/hrHence, the total time spent traveling during the day is 1+2+1 = 4 hours and the total distance traveled is 40 km

Evaluating the answer options

(A) \(\frac{2pqr}{pq+qr+pr} = \frac{2*5*10*20}{50+200+100} = \frac{2*10*2}{7}\) - Not an integer

(B) \(\frac{pqrx}{pq+qr+pr} = \frac{5*10*20*4}{50+200+100} = \frac{40*10}{35}\) - Not at integer

(C) \(\frac{2pqrx}{2pq+qr+pr} = \frac{2*5*10*20*4}{2*50 + 200 + 100} = \frac{10*2*4}{4} = 20\)

(D) \(\frac{4pqr}{2pq+qr+pr} = \frac{4*5*10*20}{400} = 20/2 = 10\)(E) \(\frac{4pqrx}{2pq+qr+pr} = \frac{4*5*10*20*4}{400} = 40\) (Option E)--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.

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