Question

Pratik takes $8$ hours to travel $36km$ downstream and return to the same spot. The speed of the boat in still water is $12km/h$. Find the speed of the current.

Answer 1

We know that,

$Speed=\frac{Distance}{Time}$

Let the Speed of current be $v$

In Downstream, Speed will be $12+v$and while he returns , speed will be $12-v$

(as Current will oppose the motion in return journey)

Total Time Taken $=8hrs$

So,

$8=\frac{36}{12+v}+\frac{36}{12-v}\Rightarrow 8=\frac{36(12-v)+36(12+v)}{144-v^2}\Rightarrow 8=\frac{2\times 36\times 12}{144-v^2}\Rightarrow 144-v^2=\frac{2\times 36\times 12}{8}\Rightarrow 144-v^2=108\Rightarrow v^2=144-108=36\Rightarrow v=6m/s$