Question

A man rows to a place $48$ km distant and back in $14$ hours. He finds that he can row $4$ km with the stream in the same time as $3$ km against the stream. The speed of the stream is

• A. $1$ km/hr
• B. $1.5$ km/hr
• C. $1.8$ km/hr
• D. $3.5$ km/hr

Answer 1

The correct option is A $1$ km/hr

Suppose man moves $4$ km downstream in $x$ hours.
Then, speed downstream $=\left(\frac{4}{x}\right)\text{km/hr}$
Speed upstream $=\left(\frac{3}{x}\right)\text{km/hr}$
According to question,
$\frac{48}{\left(4/x\right)}+\frac{48}{\left(3/x\right)}=14$
$\Rightarrow 12x+16x=14$
$\Rightarrow x=\frac{1}{2}$
So, speed downstream $=8$ km/hr
and speed upstream $=6$ km/hr
$\therefore$ Speed of the stream $=\frac{1}{2}(8-6)=1\text{km/hr}$