A fast train takes 1 hour less than a slow train for a journey of 96 km. If the speed of the slow train is 8 km/h less than that of the fast train, then find the speeds of the fast train and slow train, respectively.
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. 32 km/h, 24 km/h.
Let the speed of a fast train = x km/hr
Then slow train = (x - 8) km/hr
According to the question,
⇒
⇒ 96x - 96(x - 8) = x(x - 8)
⇒ 96x - 96x + 768 = x2 - 8x
⇒ x2 - 8x - 768 = 0
⇒ x2 - 32x + 24x - 768 = 0
⇒ x(x - 32) + 24(x - 32) = 0
⇒ (x + 24)(x - 32) = 0
⇒ x = 32
Fast = 32 km/h, Slow = 24 km/h