Question

If a train travelled 5 km/hr faster, it would take one hour less to travel 210 km. The speed of the train is:

• A. 30 km/hr
• B. 35 km/hr
• C. 70 km/hr
• D. 60 km/hr

Answer 1

The correct option is A

30 km/hr

Let the speed of the train be x km/hr.
Distance travelled = 210 km

Time taken to travel 210 km = $\frac{210}{x}$ hours

When the speed is increased by 5 km/h, the new speed is (x+5).

Time taken to travel 210 km with the new speed is $\frac{210}{x+5}$ hours.

According to the question,
$\frac{210}{x}-\frac{210}{x+5}=1$
$\Rightarrow 210(x+5)-210x=x(x+5)$
$\Rightarrow 210x+1050-210x=x^2+5x$
$\Rightarrow x^2+5x-1050=0$
$\Rightarrow x^2+35x-30x-1050=0$
$\Rightarrow x(x+35)-30(x+35)=0$
$\Rightarrow (x+35)(x-30)=0$

$\Rightarrow x=-35,30$

The speed cannot be negative. Thus, the speed of the train is 30 km/hr.