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:
Answer & explanation
Correct answer: option 2
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