Question

A boat covers 32 km upstream and 6 km downstream in 7 hr. Also it covers 40 km upstream and 48 km downstream is 9 hour. Find the speed of the boat in still water and that of the stream?

Answer 1

Let speed of boat$=x$

and speed of stream $=y$

So, Time taken in one trip will be

$\frac{32}{x-y}+\frac{6}{x+y}=7$

also

$\frac{40}{x-y}+\frac{48}{x+y}=9$

Let $\frac{1}{x-y}=A$ and $\frac{1}{x+y}=B$

So, $32A+6B=740A+48B=9$

On solving we get

$A=\frac{47}{216}$ and $B=\frac{1}{162}$

So, $x+y=162$ and $x-y=\frac{216}{47}$

On solvng we get $x=\frac{3915}{47}$ and $y=\frac{3699}{47}$