A train covered a certain distance …

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 be d km.
Since, Speed = {tex}\frac{{{\text{Distance travelled}}}}{{{\text{Time taken to travel that distance}}}}{/tex} {tex} \Rightarrow x = \frac{d}{t} \Rightarrow{/tex} d = xt ....(1)
According to the question,
x + 10 = {tex}\frac{d}{{t - 2}} \Rightarrow{/tex} (x + 10)(t - 2) = d
{tex}\Rightarrow{/tex} xt + 10t - 2x - 20 = d
{tex}\Rightarrow{/tex} -2x + 10t = 20 .....(2) [Using eq. (1)]
Again, x - 10 = {tex}\frac{d}{{t + 3}} \Rightarrow{/tex} (x - 10)(t + 3) = d
{tex}\Rightarrow{/tex} xt - 10t + 3x - 30 = d
{tex}\Rightarrow{/tex} 3x - 10t = 30 .....(3) [Using eq. (1)]
Adding equations (2) and (3), we obtain:
x = 50
Substituting the value of x in equation (2), we obtain:
(-2) {tex}\times{/tex} (50) + 10t = 20 {tex}\Rightarrow{/tex}-100 + 10t = 20
{tex}\Rightarrow{/tex}10t = 120
t = 12
From equation (1), we obtain:
d = xt = 50 {tex}\times{/tex} 12 = 600
Thus, the distance covered by the train is 600 km.