Question

A man riding a bicycle covers a distance of 36km in the direction of wind and comes back to his original position in 8 hours . If the speed of the wind is 12 km/hr . Find the speed of bicycle

Answer 1

The speed of bicycle is 17.31 km/hr

Solution:

Let "x" be the speed of bicycle

Speed of wind = 12 km/hr

Then,

x + 12 is the speed of the cycle in a direction of a wind

x - 12 is the speed of the cycle against the wind

Given that,

Distance = 36 km

Time taken = 8 hours

We know that,

$Time\ taken = \frac{distance}{speed}$

Therefore,

$\frac{36}{x + 12} + \frac{36}{x - 12} = 8\\\\36 ( \frac{1}{x + 12} + \frac{1}{x - 12}) = 8\\\\36(\frac{x - 12 + x + 12}{x^2 - 144})=8\\\\72x = 8x^2 - 1152\\\\8x^2 -72x -1152=0\\\\Solve\ by\ quadratic\ formula\\\\x = 17.31, x = -8.31\\\\Ignore\ negative value\\\\x = 17.31$

Thus speed of bicycle is 17.31 km/hr

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