A boat covers a distance of 51 km downstream in 3 hours and takes $7\frac{2}{7}$ hours to cover the same distance upstream. If the boat's speed in still water is 12 km/hrs, then the speed of the stream is:

5 km/hr

The correct answer is Option (2) → 5 km/hr

Distance $=51$ km.

Downstream time $=3$ hr.

Downstream speed $=\frac{51}{3}=17$ km/hr.

Upstream time $=7\frac{2}{7}=\frac{51}{7}$ hr.

Upstream speed $=\frac{51}{51/7}=7$ km/hr.

Let speed of boat in still water $=u$ and speed of stream $=v$.

$u+v=17$

$u-v=7$

Adding:

$2u=24 \Rightarrow u=12$

Substitute:

$12+v=17$

$v=5$

final answer: The speed of the stream is $5$ km/hr