Question

A motorboat that has a speed of 9 km/hr in still water, goes 15 km downstream and comes back in 3 hours 45 minutes. The speed of the stream is .

• A. 5 kmph
• B. 3 kmph
• C. 4 kmph
• D. 7 kmph

Answer 1

The correct option is B 3 kmph

Let $T$ and $t$ denote the time taken for downstream and upstream journeys respectively.
Then, $T+t=3\text{hrs}45\text{min}=\frac{15}{4}\text{hrs}.$
Let $v$ be the speed of the stream.
$\Rightarrow \text{Speed downstream}=9+v$ and
$\text{Speed upstream}=9-v.$
$\Rightarrow T=\frac{15}{9+v}$ ....(1) and
$t=\frac{15}{9-v}$ ...........(2)
Adding (1) and (2), we get
$\frac{15}{9+v}+\frac{15}{9-v}=T+t=\frac{15}{4}.$
$\Rightarrow \frac{1}{9+v}+\frac{1}{9-v}=\frac{1}{4}$
$\Rightarrow \frac{9-v+9+v}{81-v^2}=\frac{1}{4}$
$\Rightarrow v^2-9=0$
$\Rightarrow (v+3)(v-3)=0$
Since speed cannot be negative, we must have $v=3\text{kmph}.$
Thus, the speed of the stream is 3 kmph.