Question

A boat in the river Ganga near Rishikesh covers 24 km upstream and 36 km downstream in 6 hours while it covers 36 km upstream and 24 km downstream in $6\frac{1}{2}$ hours. Consider speed of the boat in still water be x km/hr and speed of the stream be y km/hr and answer the following questions.

Speed of boat in still water is

Answer 1

According to question,
$$\begin{array}{cc}& \frac{24}{x-y}+\frac{36}{x+y}=6\dots \dots \left(i\right)\\ & \frac{36}{x-y}+\frac{24}{x+y}=\frac{13}{2}\dots \left(ii\right).\end{array}$$
Putting $\frac{1}{x-y}=u$ and $\frac{1}{x+y}=v$
we get,
$24u+36v=6$ and $36u+24v=13/2$
Solving the above equations, we get $u=\frac{1}{8},v=\frac{1}{12}$
$\because u=\frac{1}{8}=\frac{1}{x-y}\Rightarrow x-y=8\dots$ (i)
and $v=\frac{1}{12}=\frac{1}{x+y}\Rightarrow x+y=12\dots$ (ii)
Adding equations (i) from (ii), we get $2x=20\Rightarrow x=10$
$\therefore$ Speed of boat in still water $=10km/hr$