Question

A boat goes 24 km upstream and 28 km downstream in 6 hrs. It goes 30 km upstream and 21 km downstream in $6\frac{1}{2}\mathrm{hrs}$. Find the speed of the boat in still water and also speed of the stream.

Answer 1

We have to find the speed of the boat in still water and speed of the stream

Let the speed of the boat in still water be x km/hr and the speed of the stream be y km/hr then

Speed upstream

Sped down stream

Now, Time taken to cover km down stream =

Time taken to cover km upstream =

But, total time of journey is 6 hours

Time taken to cover km upstream =

Time taken to cover km down stream =

In this case total time of journey is given to or

...(ii)

By and in equation (i) and (ii) we get

Solving these equations by cross multiplication we get

and

and

Now,

and

By solving equation and we get,

By substituting in equation we get

Hence, the speed of the stream is

The speed of boat is