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
Given:
Upstream distance = 48 km, time = 6 hours → upstream speed $v_u = 48/6 = 8$ km/hr
Downstream distance = 48 km, time = 3 hours → downstream speed $v_d = 48/3 = 16$ km/hr
Let $v$ = speed in still water, $s$ = speed of stream
Upstream: $v - s = 8$, Downstream: $v + s = 16$
Solving:
$v - s = 8$
$v + s = 16$
Adding: $2v = 24 \Rightarrow v = 12$ km/hr
Subtracting: $2s = 8 \Rightarrow s = 4$ km/hr
Average speed for the round trip = $2 \cdot 48 / (6+3) = 96/9 = 32/3$ km/hr
Check statements:
(A) $v = 12$ km/hr → False (statement says 10)
(B) $s = 4$ km/hr → False (statement says 3)
(C) Average speed = 32/3 km/hr → True
(D) Speed of stream = 4 km/hr → True