A boat can travel 36 km upstream in 5 hours. If the speed of the stream is 2.4 km/hr, how much time will the boat take to cover a distance of 78 km downstream?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 6 hours 30 minutes
Let the speed of the boat in still water be u km/hr. The upstream speed is u − 2.4 and the downstream speed is u + 2.4.
\( \displaystyle u-2.4=\frac{36}{5}=7.2 \)
\( \displaystyle u=7.2+2.4=9.6 \)
\( \displaystyle \text{Downstream speed}=9.6+2.4=12 \)
\( \displaystyle \text{Time}=\frac{78}{12}=6.5\text{ hours} \)
So the time is 6 hours 30 minutes.
Shortcut: Downstream speed = upstream speed + 2 × stream speed = 7.2 + 4.8 = 12 km/hr, so the time is 78 ÷ 12 = 6.5 hours.