Multiple choice

A man can row $\displaystyle 9\frac{1}{3}$ kmph in still water and finds that it takes him thrice as much time to row up than as to row down the same distance in the river. Find the speed of the current in kmph.

  1. $2\dfrac{12}{7}$
  2. $4\dfrac{2}{3}$
  3. $2\dfrac{6}{5}$
  4. $4\dfrac{4}{9}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Boat speed b = 28/3. Let current be c. Downstream speed = b+c, Upstream = b-c. Time taken: Upstream = 3 * Downstream. Distance/(b-c) = 3 * Distance/(b+c) => b+c = 3b-3c => 4c = 2b => c = b/2 = (28/3)/2 = 14/3 = 4 2/3.

AI explanation

Let the speed of the current be x kmph. Using the relation speed of current = speed in still water multiplied by the fraction (time difference over total time factor), the downstream speed is (28/3 + x) and upstream speed is (28/3 - x). The time taken to row up is thrice the time to row down, meaning the upstream speed is one-third of the downstream speed. Setting (28/3 - x) = (1/3) * (28/3 + x) and solving gives x = 14/3 kmph, making the speed of the current 4 and 2/3.

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