Question

A man can row $15km$ downstream in $3$ hours and $5km$ upstream in $2\frac{1}{2}$ hours. His speed in still water in $\left(km/hr\right)$ is

• A. $4km/hr$
• B. $4.5km/hr$
• C. $3.5km/hr$
• D. $5km/hr$

Answer 1

The correct option is C $3.5km/hr$

Let us assume speed still in water is x km/hr.

Speed of stream is y km/hr.

Speed of down stream

$\Rightarrow 3(x+y)$ as it is $3$hrs

$3(x+y)=15$km

$\Rightarrow x+y=5$ …….$\left(1\right)$

Speed of upstream is $2\frac{1}{2}$ hrs $\Rightarrow 2.5(x-y)$

$2.5(x-y)=5$

$\Rightarrow x-y=2$ ………$\left(2\right)$

By solving $\left(1\right)$ & $\left(2\right)$

$2x=7$

$\Rightarrow x=\frac{7}{2}$

$=3\frac{1}{2}$ km/hr

and by $\left(2\right)$

$x-y=2$

$\frac{7}{2}-y=2$

$\Rightarrow \frac{7}{2}+2=y$

$\Rightarrow y=\frac{11}{2}$

$=5\frac{1}{2}$ km/h