Question

A boat travels 30 kilometre upstream in the same amount of time it takes to travel 60 km downstream in the same river if the speed of the river is 4 kilometre per hour find the speed of the boat in still water

Answer 1

$(x + 4)60 = (x - 4)30 \\ 60x + 240 = 30x - 120 \\ 60x - 30x = - 120 - 240 \\ 30x = - 360 \\ x = \frac{360}{30} \\ 12$

Answer 2

Concept:

Stream: A river's flowing water is referred to as a stream.

Upstream - A boat is said to be moving upstream if it is moving downstream of the stream. The boat's upstream speed in this situation is its net speed.

Downstream - A boat is said to be moving downstream if it is moving in the same direction as the stream. In this instance, the boat's downstream speed is its net speed.

Still Water - In this situation, the water is regarded as being stagnant and has no speed.

Speed =distance /time

Given:

A boat travels 30 kilometre upstream in the same amount of time it takes to travel 60 km downstream in the same river if the speed of the river is 4 kilometre per hour

Find:

Find the speed of the boat in still water

Solution:

Let,speed of the boat be x

In upstream, speed=x-4km/hr

In downstream, speed=x+4 km/hr

As per question,

30/x-4 =60/x+4

⇒30(x+4) =60(x-4)

⇒30x+120 =60x - 240

⇒360=30x

⇒x=12 km/hr

Therefore, the speed of the boat in still water =12km/hr

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