A fisherman is rowing a boat. He takes 6 hours to row 48 km upstream whereas he takes 3 hours to go to the same distance downstream.
Based on the above information, which of the following are correct?
(A) His speed of rowing in still water is 10 km/hour.
(B) The speed of the stream is 3 km/hour.
(C) The average speed of the fisherman is 32/3 km/hour.
(D) The speed of the stream is 4 km/hour.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (C) and (D) only
Let u be his speed in still water and v the speed of the stream (km/hour). Upstream the speeds subtract; downstream they add:
\( \displaystyle u - v = \frac{48}{6} = 8 \)
\( \displaystyle u + v = \frac{48}{3} = 16 \)
\( \displaystyle u = \frac{16 + 8}{2} = 12 \)
\( \displaystyle v = \frac{16 - 8}{2} = 4 \)
So his speed in still water is 12 km/hour and the speed of the stream is 4 km/hour.
Checking the statements
(A) His speed of rowing in still water is 10 km/hour. — Incorrect. It is 12 km/hour.
(B) The speed of the stream is 3 km/hour. — Incorrect. It is 4 km/hour.
(C) The average speed of the fisherman is 32/3 km/hour. — Correct. Average speed = total distance ÷ total time:
\( \displaystyle \frac{48 + 48}{6 + 3} = \frac{96}{9} = \frac{32}{3} \text{ km/hour} \)
(D) The speed of the stream is 4 km/hour. — Correct. v is 4 km/hour.
Tip: For a round trip, the average speed is total distance ÷ total time, not the simple average of the two speeds, \((8 + 16)/2 = 12\).