Question

Question 3
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.

Answer 1

Let the speed of the train be x km/h and the time taken by train to travel the given distance be t hours and the distance to travel was d km. We know that,
$\text{Speed}=\frac{\text{Distance travelled}}{\text{Time taken to travel that distance}}$
$x=\frac{d}{t}$
Or, d = xt ----- (i)
Using the information given in the question, we obtain
$(x+10)=\frac{d}{(t-2)}$
$(x+10)(t-2)=d$
$xt+10t-2x-20=d$
By using equation (i), we obtain
-2x + 10t = 20 ----- (ii)
$(x-10)=\frac{d}{(t+3)}$
(x-10) (t+3) = d
xt-10t+3x-30 =d
By using equation (i), we obtain
3x - 10t = 30 ----- (iii)
Adding equations (ii) and (iii), we obtain
x = 50
Using equation (ii), we obtain
(-2) $\times$ (50) + 10t = 20
-100 + 10t = 20
10t = 120
t = 12 hours
From equation (i), we obtain
Distance to travel = d = xt
= 50 $\times$ 12
= 600 km
Hence, the distance covered by the train is 600 km.