Question

Find the speed of the train.

Answer 1

Step-by-step explanation:

Distance given is 480 km

1st case

Let the speed be x km / hr

Time = Distance / time

= 480/x hr

2nd case

Again, speed = (x-8)km/hr

Time = 480/(x-8) hr

According to question,

480/x - 480/(x-8) = 3

=> 480(x-8) - 480x / x (x-8) = 3

=> 480x - 3840 - 480x = 3x (x-8)

=>-3480 = 3x^2 - 24x

or 3x^2 - 24x = - 3840

=> 3x^2 - 24x + 3840 = 0

=> 3(x^2 - 8x + 1280) = 0

=> x^2 - (40-32)x + 1280 = 0

=> x^2 - 40x + 32x +1280 = 0

=> x (x-40) + 32 (x-40) = 0

=> (x-40) (x+32) = 0

Speed of train = 40 km / hr in first case and (40-8) ie 32 km / hr in second

Hope it helps.....