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The rate at which a river flows is one-third the speed of a boat in still water. If that boat travels down the river for 2 hours and then back up river for 2 hours, it will be 16 km short of its starting point. The speed (km/hour) of the boat in still water is

A) 4
B) 6
C) 8
D) 12

Correct Answer:




D) 12

Description for Correct answer:
Speed of boat in still water = kmph.

Speed of current = \( \Large \frac{x}{3} \ kmph \)

\( \Large \therefore \) Speed downstream

= \( \Large x + \frac{x}{3} = \frac{4x}{3} \ kmph \)

Speed upstream

= \( \Large x - \frac{x}{3} = \frac{2x}{3} \ kmph \)

\( \Large \therefore \frac{4x}{3} \times 2 - \frac{2x}{3} \times 2 = 16 \)

=> \( \Large \frac{4x}{3} = 16 \)

=> \( \Large x = \frac{16 \times 3}{4} = 12 \ kmph \)

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