Question

A man can row $9\frac{1}{3}\mathrm{km}/\mathrm{h}$ in still water and finds that it takes him twice as much time to row up then as to row down the same distance in the river. Based on above information, answer the following questions.
The speed of the boat in upstream is

• A. $14\mathrm{km}/\mathrm{h}$
• B. $\frac{28}{3}\mathrm{km}/\mathrm{h}$
• C. $\frac{14}{3}\mathrm{km}/\mathrm{h}$
• D. $\frac{7}{3}\mathrm{km}/\mathrm{h}$

Answer 1

Answer: (C)

Given;
Speed of boat in still water, $b=\frac{28}{3}\mathrm{km}/\mathrm{h}$
Let, ' $S$ ' be the speed of stream and also given, Time in upstream $=3\times$ time in downstream.
Downstream distance $=$ upstream distance $=\mathrm{d}$
And, upstream speed of boat $=\mathrm{b}-\mathrm{s}$
Downstream speed of boat $=b+s$
$\therefore$ Time in upstream $=3\times$ time in downstream
$\Rightarrow \frac{d}{b-s}=3\left(\frac{d}{b+s}\right)$
$\Rightarrow b+s=3(b-s)$
$\Rightarrow 2b=4\mathrm{s}$
$\Rightarrow 2\times \frac{28}{3}=4\mathrm{s}$
$\Rightarrow s=\frac{56}{3\times 4}=\frac{14}{3}\mathrm{km}/\mathrm{h}$
$\therefore$ Speed of stream $=\frac{14}{3}\mathrm{km}/\mathrm{h}$
(i) So, speed of boat in upstream
$=\mathrm{b}-\mathrm{s}$
$=\frac{28}{3}-\frac{14}{3}=\frac{14}{3}\mathrm{km}/\mathrm{h}$