Question

A train moving with uniform speed for a certain distance takes 6 hours less if its speed be
increased by 6 km/hour. It would have taken 6 hours more, had its speed been decreasedby 4 km/hr. Find the distance travelled of the journey and the speed of the train.

Answer 1

From formula 
D=st
given
D=(s+6)(t-4)=st-4s+6t-24.......>1
D=(s-6)(t+6)=st+6s-6t-36)......>2

from 1&2 
-4s+6t=24
6s-6t=36 .....>3

on solving 
2s=60 ==> s=30 km/h
(3)==> 6(30)-6t=36
t= 24 h
.
. . D=30(24) = 720 km


Ans: D= 720 km

Answer 2

Hey mate!!

Let the distance be y km / hr and speed be x km / hr

Scheduled time = y / x

Now,

y / ( x + 6) = (y / x) - 6

= 6x^2 + 36x = 6y

x^2 + 6x = y

Now,

y / ( x - 4) = (y / x) + 6

= 4y = 6x^2 - 24x

2y = 3x^2 -12x

2(x^2+6x) = 3x^2 - 12x

2x^2 + 12x = 3x^2 - 12x

24x = x^2

x = 24

So speed of train is 24 km / hr

Distance = x^2 + 6x = y

= 24^2 + 6*24 = y

= 720 km

#Thank u !