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.

Answer 1

Let the speed of the train be $xkm/h$ and the time taken by train to travel the given distance be $t$ hours and the distance to travel be $dkm$. We know that,

$\Rightarrow$$Speed=\frac{Distance}{Time}$

$\Rightarrow$$x=\frac{d}{t}$

$\therefore d=xt$.......(i)

Case 1

$\Rightarrow$$(x+10)\times (t-2)=d$

$\Rightarrow$$xt+10t-2x-20=d$

$\Rightarrow$$d+10t-2x-20=d$

$\Rightarrow$$-2x+10t=20$...... (ii)

Case 2

$\Rightarrow$$(x-10)\times (t+3)=d$

$\Rightarrow$$xt-10t+3x-30=d$

$\Rightarrow$$d-10t+3x-30=d$

$\Rightarrow$$3x-10t=30$......... (iii)

Adding equations (ii) and (iii), we gets

$\Rightarrow x=50$

Substitute the value of x in (ii) we gets

$\Rightarrow (-2)\times \left(50\right)+10t=20$

$\Rightarrow -100+10t=20$

$\Rightarrow 10t=120$

$\Rightarrow t=12$ hours

Substitue the value of $t$ and $x$ in equation (i), we gets

Distance to travel $=d=xt$

$\Rightarrow d=12\times 50=600$Km

Hence, the distance covered by the train is $600km.$