Question

A swimmer jumps from a bridge over a canal and swims $1\text{km}$ up stream. After that first $\text{km}$, he passes a floating cork. He continues swimming for half an hour and then turns around and swims back to the bridge. The swimmer and the cork reach the bridge at the same time. The swimmer has been swimming at a constant speed. How fast does the water in the canal flow in $\text{km/hr}$?

Answer 1

Let the speed of the canal be $u$ and that of swimmer with respect to water is $v$.
Time taken by the cork to reach the bridge $t=\frac{1}{u}\text{h}$.

The same time taken by the swimmer
$=$ Half hour + time taken to cover distance travelled (while going up + 1 km to reach the bridge)
$=\frac{1}{2}hr+\frac{\text{Distance travelled}}{\text{Velocity downstream}}$

$\Rightarrow \frac{1}{2}+\frac{1+\frac{v-u}{2}}{v+u}=\frac{1}{u}$

$\Rightarrow \frac{1}{2}+\frac{2+v-u}{2(v+u)}=\frac{1}{u}$

$\Rightarrow \frac{(v+u+2+v-u)}{2(v+u)}=\frac{1}{u}$

$\Rightarrow (2v+2)u=2(v+u)$
$\Rightarrow 2vu+2u=2v+2u$
$u=1\text{km/hr}$