Question

A boat sails a distance of $44km$ in $4$ hours with the current. It takes $4$ hours $48$ minutes longer to cover the same distance against the current. Find the speed of the boat in still water and the speed of the current.

Answer 1

Let the speed of the boat in still water be $4$ km/hr and speed of stream be $v$km/hr.

Speed down the stream $=u+v$

Speed against the stream $=u–v$

Now,Downstream distance $=$Speed down the stream$\times$ Time taken

$\Rightarrow 40=2(u+v)$

$\Rightarrow u+v=20$

$\Rightarrow u=20–v$

Upstream distance$=$Speed against the stream$\times$ Time taken

$\Rightarrow 40=(u–v)\times 4$

$\Rightarrow u–v=10$

$\Rightarrow 20–v–v=10$

$\Rightarrow 20–2v=10$

$\Rightarrow 2v=20–10$

$\Rightarrow 2v=10$

$\Rightarrow v=5$ km/hr

$u=20–5=15$ km/hr

Thus speed of the boat in still water is $15$ km/hr and speed of stream is $5$ km/hr.