Question

A steamer goes downstream and covers the distance between two parts in 4 hours while it covers the same distance upstream in 5 hours. If the speed of the stream is 2 km/h, find the speed of the steamer in still water.

Answer 1

Let the two parts are A and B

A _____________________ B

Let the speed of streamer is x km / hr ,

$\large{ \mathbf{ \underline{ when \:\: going\: \:towards \:\: upstream }}}$

As the streamer is going towards the stream, speed of streamer will decrease because stream will work like a hurdle , New speed will be ( x -  2 )  km/hr

$Speed =  \dfrac{Distance}{ Time } \\ \\ \\ x - 2 = \dfrac{ Distance }{ 5 } \\ \\ \\ 5( x - 2 ) = Distance \:\:\:\:\:\:\:\:\:\:-------: ( 1 )$

$\maths{ \underline{\bold{ when going towards downstream }}}$

As streamer is going along with the stream, speed of streamer will increase, New speed will be ( x + 2 ) km/hr

$Speed = \dfrac{ Distance }{ time } \\ \\ \\ ( x + 2 ) = \dfrac{Distance}{ 4 } \\ \\ \\  4( x + 2 ) = Distance \:\:\:\:\:\:\:\:\:\: ------: ( 2 )$

Distance between A and B cant be changed , so

1 eq = 2 eq

5( x - 2 ) = 4( x + 2 )

5x - 12 = 4x + 8

5x - 4 = 8 + 10

x = 18

Hence, Speed of Streamer = x km/hr = 18 km/hr

Answer 2

Speed of the stream = 2 km/h

Let the speed of the steamer in still water be x km/h

Upstream:

Speed = (x - 2) km/h

Distance = Speed x Time

Distance = 5(x - 2) km

Downstream:

Speed = (x + 2) km/h

Distance = Speed x Time

Distance = 4(x + 2) km

Solve x:

Since the distance for the upstream and downstream is the same:

5( x - 2) = 4( x + 2)

5x - 10 = 4x + 8

x = 18 km/h

Answer: The speed of the steamer is 18 km/h