Question

A steamer goes downstream and covers the distance between two ports in 4 hours. It covers same distance in 6 hours then it goes upstream if the stream flows at,2km/hr , then find what is the speed of streamer in still water?​

Answer 1

Given :

• Time taken to cover the distance between two ports downstream = 4 hours

• Time Taken to cover the distance between two ports upstream = 6 hours

• Speed of stream = 2 km/h

To find :

Speed of the steamer .

Solution :

Let the speed of the steamer be x km/h.

So, the speed of the steamer downstream will be (x + 2) km/h

And the speed of steamer upstream will be (x - 2) km/h.

Distance covered by the steamer downstream from Port A to B :

We know that :

$\bf{Speed = {Distance}{time}}$

Using the above formula and substituting the values in it , we get :

$:\implies \bf{(x + 2) = {Distance}{4}}$

$:\implies \bf{(x + 2) \times 4 = d}$

$:\implies \bf{4(x + 2) = d}$

$\boxed{\therefore \bf{d = 4(x + 2)}}$

Hence, the distance covered from Port A to B is 4(x + 2) km/h

Distance covered by the steamer upstream from Point A to B :

We know that :

$\bf{Speed = {Distance}{time}}$

Using the above formula and substituting the values in it , we get :

$:\implies \bf{(x - 2) = {Distance}{6}}$

$:\implies \bf{(x - 2) \times 6 = d}$

$:\implies \bf{6(x - 2) = d}$

$\boxed{\therefore \bf{d = 6(x - 2)}}$

Hence the speed of the steamer upstream from Point A to B is 6(x - 2) km/h

Now , According to the Question , we know that the distance covered will be same in both the upstream and downstream.

Hence by making the two Equations equal , we get :

$\boxed{\bf{4(x + 2) = 6(x - 2)}}$

$:\implies \bf{4x + 8 = 6x - 12}$

$:\implies \bf{4x - 6x = - 12 - 8}$

$:\implies \bf{-2x = - 20}$

$:\implies \bf{\not{-}2x = \not{-}20}$

$:\implies \bf{2x = 20}$

$:\implies \bf{x = \dfrac{20}{2}}$

$:\implies \bf{x = 10}$

$\boxed{\therefore \bf{x = 10}}$

Hence the speed of the steamer in still water is 10 km/h.