Question

A boat covers a certain distance downstream in 5 hours but it takes 11 hours to cover the same distance upstream. If the speed of the stream is 3 km/hr, find is the speed of the boat in still water.(in km/hr)

Answer 1

Find the speed of the boat in still water when the speed of the stream is 3 km/hr:

Let the speed of the boat in still water be $x$ km/hr.

It is given that the speed of the stream is 3 km/hr.

$\therefore$Upstream speed $=x-3\text{km/hr}$.

$\therefore$Downstream speed $=x+3\text{km/hr}$.

We know that,

$\text{Distance}=\text{Time}\times \text{Speed}$.

Also given that a boat covers a certain distance downstream in 5 hours but it takes 11 hours to cover the same distance upstream.

$\begin{array}{rcl}5\left(x+3\right)& =& 11\left(x-3\right)\\ & \Rightarrow & 5x+15=11x-33\\ & \Rightarrow & 6x=48\\ & \Rightarrow & x=8\end{array}$

Hence, the speed of the boat in still water is $8\text{km/hr}$.