The ratio of the speed of a motorboat and that of the current of water is 14 : 8. The boat goes a certain distance along with the current in 3 hours 12 minutes. How much time does it take to come back?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 11 hours 44 minutes
Let the speed of the boat in still water be 14k and the speed of the current 8k.
\( \displaystyle \text{Downstream speed}=14k+8k=22k \)
\( \displaystyle \text{Upstream speed}=14k-8k=6k \)
For the same distance, time is inversely proportional to speed. Downstream time = 3 hours 12 minutes = 3.2 hours.
\( \displaystyle \text{Upstream time}=3.2\times\frac{22k}{6k} \)
\( \displaystyle =\frac{3.2\times 11}{3} \)
\( \displaystyle =\frac{35.2}{3}\text{ hours} \)
\( \displaystyle \frac{35.2}{3}=11\frac{2.2}{3}\text{ hours} \)
\( \displaystyle \frac{2.2}{3}\times 60=44\text{ minutes} \)
So the boat takes 11 hours 44 minutes to come back.