A motor boat can travel 5 km/hr in still water. It travelled 9 km downstream in river and then returned back taking altogether 10 hours. The rate of flow of water in the river is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 4 km/hr
Let the speed of the stream be v km/hr (v < 5, or the boat could not return).
\( \displaystyle \text{Downstream speed}=5+v \)
\( \displaystyle \text{Upstream speed}=5-v \)
Total time = time downstream + time upstream:
\( \displaystyle \frac{9}{5+v}+\frac{9}{5-v}=10 \)
\( \displaystyle \frac{9(5-v)+9(5+v)}{25-v^2}=10 \)
\( \displaystyle \frac{90}{25-v^2}=10 \)
\( \displaystyle 25-v^2=9 \)
\( \displaystyle v^2=16\ \Rightarrow\ v=4\ \text{km/hr} \)
Shortcut: Substitute the options. v = 4 gives \( \frac{9}{9}+\frac{9}{1}=10 \) hours. v = 6 is impossible (the upstream speed would be negative), v = 3.5 gives about 7.06 hours and v = 3 gives 5.625 hours.