Jyoti can row a boat at \(7\frac{1}{2}\) km/h in still water. If in a river running at 1.5 km/h, she takes 50 minutes to row to a place A and come back, then how far off is the place A?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 3 km
Going with the current, the river’s speed adds to the boat’s speed; going against it, it is taken away. The times for the two ways add up to 50 minutes. Let the place A be \(d\) km away.
The two speeds:
Downstream: \(7.5+1.5=9\) km/h
Upstream: \(7.5-1.5=6\) km/h
The total time (50 minutes \(=\frac{50}{60}=\frac{5}{6}\) h):
\(\displaystyle\frac{d}{9}+\frac{d}{6}=\frac{5}{6}\)
\(\displaystyle\frac{2d+3d}{18}=\frac{5}{6}\), so \(5d=15\)
\(d=3\) km