In a journey of 500 km, the train was slowed down due to bad weather. Its average speed for the trip was reduced by 100 km/hr and the time of journey increased by 45 minutes. What is the duration of the journey in normal weather conditions?
Let the duration of the journey = t hours.
old time : new time = t : t + 45/60 = t : t + ¾
⇒ old speed : new speed = t + 3/4 ? t
(t + ¾) : t = 500/t ? (500/t – 100)
t + ¾ = 5/((5/t) – 1)
(t + ¾) (5 – t) = 5t
5t – t2 + 15/4 – 3t/4 = 5t
t2 – 15/4 + 3t/4 = 0
4t2 + 3t – 15 = 0
t = 1.6 hours