Question

A boat take $6$ hours to travel $36km$ downstream and $24km$ upstream. It take $9$ hours to travel $48km$ downstream and $40km$ upstream. Find the speed of the stream and that of boat in still water.

Answer 1

Let the speed of boat in still water$=x$

Let the speed of stream$=y$

Upstream speed=speed of boat-speed of stream$=x-y$

Downstream speed=speed of boat+speed of stream$=x+y$

Given,

$\frac{36}{x+y}+\frac{24}{x-y}=\mathrm{6............}\left(1\right)$

$\frac{48}{x+y}+\frac{40}{x-y}=\mathrm{6............}\left(2\right)$

Mulply (1) by 5 ang (2) by 3 we get

$\frac{180}{x+y}+\frac{120}{x-y}=\mathrm{30.........}\left(3\right)$

$\frac{144}{x+y}+\frac{120}{x-y}=\mathrm{27.........}\left(4\right)$

Subtract above equations

$\frac{36}{x+y}=3$

$x+y=\mathrm{12.....}\left(a\right)$

Put (a) in (4) we get

$\frac{144}{12}+\frac{120}{x-y}=27$

$12+\frac{120}{x-y}=27$

$x-y=\mathrm{8.....}\left(b\right)$

Adding $\left(a\right)$ and $\left(b\right)$ we get

$2x=20$

$x=10$

Put $x$ in $\left(a\right)$ we get

$10+y=12$

$y=2$

Therefore,

Speed of boat in still water$=10kmph$

Speed of stream$=2kmph$