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.

If $u=\frac{1}{x-y}$ and $v=\frac{1}{x+y}$, then $u=$

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 $36u+24v=\frac{13}{2}$
Solving the above equations, we get $u=\frac{1}{8},v=\frac{1}{12}$