Let the speed of train be xkm∕h and actual time taken is t hrs. In first case, distance =(x+6)(t−4)km ...(i) In second case, distance =(x−6)(t+6)km ...(ii) Also distance =xt from (i) and (ii) (x+6)(t−4)=(x−6)(t+6) ...(iii) ⇒
x+6
x−6
=
t+6
t−4
⇒
x
6
=
2t+2
10
⇒
x
6
=
t+1
5
⇒ 5x=6t+6⇒5x−6t=6 ⇒ t=
5x−6
6
Putting the value of 't' in eqn. (iii), we get x=30km∕hr ∴ t=24hr Thus, distance =30×24=720