Question

A car covers a distance of 240 km with some speed. If the speed is increased by 20km/hr, it will cover the same distance in 2 hours less. Find the speed of the car.

Answer 1

Let the speed of the car be x km/hr.
Then, the time taken by the car to complete 240 km will be $\frac{\mathrm{Distance}}{\mathrm{Speed}}$ = $\frac{240}{x}$ hr.
Now, if the speed of the car is increased by 20 km/hr, then the time taken to complete 240 km will be $\frac{\mathrm{Distance}}{\mathrm{Speed}}$ =$\frac{240}{x+20}$ hr.
By the given condition, we get:
$$\begin{gathered} \frac{240}{x}-\frac{240}{x+20}=2 \\ \Rightarrow 240\left[\frac{x+20-x}{x\left(x+20\right)}\right]=2 \\ \Rightarrow \frac{20}{x^2+20x}=\frac{1}{120} \end{gathered}$$
$\Rightarrow$ x² + 20x = 2400
$\Rightarrow$ x² + 20x – 2400 = 0
On splitting the middle term 20x as 60x – 40x, we get:
x² + 60x – 40x – 2400 = 0
$\Rightarrow$ x(x + 60) – 40(x + 60) = 0
$\Rightarrow$ (x + 60)(x – 40) = 0
$\Rightarrow$ x + 60 = 0 or x – 40 = 0
$\Rightarrow$ x = – 60 or x = 40
Since x is the speed of the car, which cannot be negative, x = 40.
Thus, the speed of the car is 40 km/hr.