Boats and Streams Formula

In this class, We discuss Boats and Streams Formula.

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The reader should have prior knowledge of the speed and distance formula. Click Here.

The below diagram shows the water flow.

We call the direction in which water is moving downstream.

We call the direction opposite to the water flow is called upstream.

Formulae:

1) If the boat’s speed in still water is u kmph and the speed of the stream is v kmph, then.

Speed of the boat in downstream = (u+v) kmph

Speed of the boat in upstream = (u-v) kmph.

Towards downstream, the water flow helps the boat move faster, so u + v kmph.

Towards upstream, the boat going against to water flow will reduce the speed. So u – v kmph.

2) If the upstream speed is a kmph and the downstream speed is b kmph, then.

speed in still water = 1/2(a+b) kmph

Speed of the stream = 1/(a-b) kmph.

Understand the process of how we got the formulae. The process helps you to solve the bits.

Procedure:

Downstream is a kmph.

Upstream is b kmph.

Assume the speed of the boat is x kmph.

The speed of the stream is y kmph.

From the above formulae x + y = a equation 1

x – y = b equation 2.

adding both the equations qe get 2x = a+b

x = 1/2(a+b) = speed of the boat in still water.

Subtracting both the equations, we get 2y = a-b

y = 1/2(a-b) = speed of the stream.

Important: Given downstream and upstream speeds, we can find the boat’s speed in still water and speed of the stream.