A boat goes upstream and downstream in . It goes upstream and downstream in hours. Find the speed of the boat in still water and also speed of the stream.

Let’s assume,

The speed of the boat in still water as

And,

The speed of the stream as

We know that,

Speed of the boat in upstream

Speed of the boat in downstream

So, time taken to cover 28 km downstream [∵ time = distance/ speed]

Time taken to cover 24 km upstream [∵ time = distance/ speed]

It’s given that the total time of journey is 6 hours. So, this can expressed as

…… (i)

Similarly,

Time taken to cover 30 km upstream [∵ time = distance/ speed]

Time taken to cover 21km downstream [∵ time = distance/ speed]

And for this case the total time of the journey is given as 6.5 i.e hours.

Hence, we can write

….. (ii)

Hence, CD solving (i) and (ii) we get the required solution

Taking,  and  in equations (i) and (ii) we have (after rearranging)

 …… (iii)

 ……. (iv)

Solving these equations CD cross multiplication we get,

and

Now,

…. (v)

……. (vi)

On Solving (v) and (vi)

Adding (v) and (vi), we get

⇒

Using in (v), we find D

⇒

Therefore,

Speed of the stream .

Speed of boat .