Question

A man can row three quarters of a km against the stream in $11\frac{1}{4}minutes$ and return in $7\frac{1}{2}minutes$. The speed of the man in still water is

• A. 2 km/h
• B. 3 km/h
• C. 4 km/h
• D. 5 km/h

Answer 1

The correct option is D 5 km/h

We can write three-quarters of a kilometre as $750$ metres and $11\frac{1}{4}$ minutes as $675$ seconds.

Rate upstream is:

$\frac{750}{675}=\frac{10}{9}$ m/sec.

Rate downstream is:

$\frac{750}{450}=\frac{5}{3}$ m/sec.

Therefore, rate in still water is:

$speedinstillwater=\frac{upstreamspeed}{downstreamspeed}$

$Speedofmaninstillwater=\frac{upstreamspeed+downstream}{2}$

$\frac{1}{2}(\frac{10}{9}+\frac{5}{3})=\frac{1}{2}(\frac{10}{9}+\frac{15}{9})=\frac{1}{2}\left(\frac{10+15}{9}\right)=\frac{1}{2}\times \frac{25}{9}=\frac{25}{18}$ m/sec.

Now, we convert m/sec into km/hr. as follows:

$\frac{25}{18}\times \frac{18}{5}=5$ km/hr.

Hence, the speed of the man in still water $5$km/hr.