Question

A train covered a certain distance at a uniform speed. If the train could have been 10 km/hr. faster, it would have taken 2 hours less than the scheduled time. And,if the train were slower by 10 km/hr;if would have taken 3 hours more than the scheduled time. Find the distance covered by the train.

Answer 1

Let, distance=x km and uniform speed=y km/hr

Then, $\frac{x}{y}$ - $\frac{x}{y+10}$ = 2 or 10x = 2y(y+10) ….(i)

And, $\frac{x}{y-10}$ - $\frac{x}{y}$ = 3 or 10x = 3y(y-10) ….(ii)

on dividing (i) by (ii), we get,

$\frac{10x}{10x}$ = $\frac{2y(y+10)}{3y(y-10)}$ i.e. 3y-30 = 2y+20; y = 50

Substituting the value of y in eq. (i), we get,

10x= 2 $\times$50(50+10)= 100$\times$60 = 6000

$\Rightarrow$ x= $\frac{6000}{10}$ = 600 km

Thus, distance covered by train is 600 km.