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

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

## Solution:

Let the speed of the train be $$x \text{km/h}$$, time be $$t \text{hours}$$, and the distance be $$d \text{km}$$ $d = x \times t \quad \text{(i)}$ Case 1: Speed is $$x + 10 \text{km/h}$$ and time is $$t – 2 \text{hours}$$ $-2x + 10t = 20 \quad \text{(ii)}$ Case 2: Speed is $$x – 10 \text{km/h}$$ and time is $$t + 3 \text{hours}$$ $3x – 10t = 30 \quad \text{(iii)}$ Adding equations (ii) and (iii) to solve for $$x$$ $x = 50 \text{km/h}$ Substituting the value of $$x$$ into equation (ii) to find $$t$$ $10t = 120 \Rightarrow t = 12 \text{hours}$ Substituting the value of $$t$$ and $$x$$ into equation (i) to find $$d$$ $d = 12 \times 50 = 600 \text{Km}$ Hence, the distance covered by the train is 600km.