Question

The speed of an express train is x km/h and the speed of an ordinary train is 12 km/h less than that of the express train. If the ordinary train takes one hour longer than the express train to cover a distance of 240 km, find the speed of the express train. [4 MARKS]

Answer 1

Framing the equation: 1 Mark
Steps: 2 Marks
Answer: 1 Mark

Let the speed of express train be x km/h Then the speed of ordinary train will be (x-12) km/h.
Time taken by express train =$\frac{240}{x}h$
Time taken by ordinary train $=\frac{240}{x-12}h$
According to the question,
$\frac{240}{x-12}-\frac{240}{x}=1\Rightarrow \frac{240x-240x+2880}{(x-12)\left(x\right)}=1$
$\Rightarrow 2880=x^2-12x\Rightarrow x^2-60x+48x-2880=0\Rightarrow x(x-60)+48(x-60)=0\Rightarrow (x-60)(x+48)=0$
Either x - 60 = 0 or x + 48 = 0
$\Rightarrow x=60$ or x = $-48$
Since the speed cannot be negative, so we reject x = $-48$.
Hence the speed of the express train is 60 km/h.