Question

A man riding on a bicycle covers a distance of 60 km in a direction of wind comes back to his original position in 8 hours. If the speed of the winds is 10km/hr. find the speed of the bicycle.

Answer 1

It is given that the speed of the wind is 10 km/hr.
Let the speed of the bicycle be x km/hr.
Then, the speed of the bicycle in the direction of the wind will be (x + 10) km/hr and the speed of the bicycle against the direction of the wind will be (x – 10) km/hr.
Time taken to cover 60 km in the direction of the wind = $\frac{\mathrm{distance}}{\mathrm{speed}}=\frac{60}{x+10}$
Time taken to cover 60 km against the direction of the wind = $\frac{\mathrm{distance}}{\mathrm{speed}}=\frac{60}{x-10}$
Thus, by the given condition, we get:
$$\begin{gathered} \frac{60}{x+10}+\frac{60}{x-10}=8 \\ \Rightarrow 60\left[\frac{x-10+x+10}{\left(x+10\right)\left(x-10\right)}\right]=8 \\ \Rightarrow 15\left[\frac{2x}{x^2-100}\right]=2 \\ \Rightarrow \frac{15x}{x^2-100}=1 \end{gathered}$$
$\Rightarrow$ x² – 100 = 15x
$\Rightarrow$ x² – 15x – 100 = 0
On splitting the middle term –15x as 5x – 20x, we get:
x² + 5x – 20x – 100 = 0
$\Rightarrow$ x(x + 5) – 20(x + 5) = 0
$\Rightarrow$(x + 5)(x – 20) = 0
$\Rightarrow$ x + 5 = 0 or x – 20 = 0
$\Rightarrow$ x = –5 or x = 20
Since x is the speed of the bicycle, which cannot be negative, x = 20.
Thus, the speed of the bicycle is 20 km/hr.