Question

A train travels a distance of 480 km at a uniform speed if the speed has been 8 km per hour less than it would have taken 3 hours more to cover the same distance we need to find speed of the train

Answer 1

let the speed of train = x
and the time taken = t
as speed = distance /time
           x = 480 / t
or        t = 480 / x
or       xt = 480
 when speed is 8 km/hr less then new speed X = x-8
  then time is increased so, new time T = t+3

now X * T =480
 (x-8) * (t+3) =480
xt+3x-8t-24 = 480
480 + 3x - 8 * 480/x =480
take lcm
3x^2 - 3840 = 24x
transpose 24x at LHS and div. the eq. by3
x^2 - 8x -1280 =0
x^2 -40x+32x - 1280 =0                                 (by mid. term splitting)
(x-40) (x+32)=0
so, x=40
or x=-32 which is not possible as speed can never be neg.
so the speed of train was 40 km/hr