5. An express train takes 3 hours less than a passenger train for a journey of 600 km. if
the speed of the passenger train was 10 km/hr. less than that of the express train,
find the speed of both the trains.
Answers
Answer:
Sorry but don't actually know the answer.
The speed of the express train is 50 km/hr and the speed of the passenger train is 40 km/hr.
Let us consider the speed of the express train to be x km/hr
Given that the speed of the passenger train is 10km/hr less than that of passenger train.
So, speed of passenger train = (x-10) km/hr
Total distance to cover = 600km
Time taken by express train = 600/x hrs
Time taken by passenger train = 600/(x-10) hrs
Given that the difference in the time taken is 3 hours.
So,
600/(x-10) - 600/x = 3
⇒ (600x-600x+6000) = 3x(x-10)
⇒ 6000 = 3x²-30x
⇒ 3x²-30x-6000 = 0
⇒ x² - 10x - 2000 = 0
⇒ x² - 50x + 40x - 2000 = 0
⇒ x(x-50) + 40(x-50) = 0
⇒ (x-50)(x+40) = 0
By Zero Product Rule,
x = 40 cant be true as speed cant be negative
So, x = 50
Speed of the express train = 50 km/hr
Speed of the passenger train = 50-10 = 40 km/hr