Question

A steamer goes downstream and covers the distance between two ports in 5 hours, while it covers the same distance upstream in 6 hours. If the speed of the stream is 1 km/h, then find the speed of the steamer in still water.​

Answer 1

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

Then, the speed downstream =(x+2) km/h

and the speed upstream =(x−2) km/h

Given, distance covered in 4 hours downstream = distance covered in 5 hours upstream

∴4(x+2)=5(x−2)

⇒4x+8=5x−10

⟹4x−5x=−10−8

[Transposing 5x to LHS and 8 to RHS]

⟹−x=−18 or x=18km/h

Answer 2

SOLUTION :-

Given that,

Speed of the stream = 1 km/h

Let,

Speed of the steamer in still water = x

Downstream :-

Speed downstream = ( x + 1 ) km/h

Time taken = 5h

Distance between two ports = 5 ( x + 1 ) km

Upstream :-

Speed upstream - ( x - 1 ) km/h

Time taken = 6h

Distance between two ports = 6 ( x - 1 ) km

According to the question,

$\longrightarrow\sf 5(x+1) = 6(x-1) \\\\\longrightarrow 5x+5= 6x-6 \\\\\longrightarrow 5x-6x= -6-5 \\\\\longrightarrow -x = - 11 \\\\\longrightarrow \bf x = 11$

Speed of the streamer in still water = 11 km/h