Question

A swimmer jumps from a bridge over a canal and swims 1 km upstream. After that first km, he passes a floating cork. He continues swimming for half an hour and then turns around 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 w.r.t water. If speed of water in canal is X km/hr., then X is

Answer 1

Let $V_w=u\&V_{sw}=v$
Time taken by swimmer to go from M to O and O to A = time taken by cork to reach A from M

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