Question

A train covers a distance of 480 km at a uniform speed. If speed had been 8km /hr less then it would have taken 3 hours more to cover the same distance. Find the usual speed of the train.

Answer 1

Distance travelled by the train = 480 km
Let the speed of the train be x kmph
Time taken for the journey = 480/x
Given speed is decreased by 8 kmph
Hence the new speed of train = (x – 8) kmph
Time taken for the journey = 480/(x – 8)
$\frac{480}{x-8}-\frac{480}{x}=3$
$\frac{480(x-x+8)}{x(x-8)}$
$\frac{480\times 8}{3}=x^2-8x$
$1280=x^2–8x$
$x^2–8x–1280=0$
On solving we get x = 40
Thus the speed of train is 40 kmph