A passenger train left town alpha for town beta. At the same time, a goods train left beta for alpha. The speed of each train is constant throughout the whole trip. Two hours after the trains met, they were 450 km apart. The passenger train arrived at the place of destination 16 hours after their meeting and the goods train, 25 hours after the meeting. How long did it take the passenger train to make the whole trip?
Answers
The time taken by the passenger train to make the whole trip is 36 hours.
Step-by-step explanation:
Let speed of passenger train be X
Let speed of goods train be Y
Let the trains met after Z hours .
X + Y = 225 → equation (1)
Now,
ZY/X = 16 → equation (2)
ZX/Y = 25 → equation (3)
On dividing equation (2) by equation (3), we get,
X:Y = 5:4 → equation (4)
In substituting equation (4) in (1), we get,
X/Y = 5/4 ⇒ X = 5Y/4
The equation (1) becomes,
5Y/4 + Y = 225 ⇒ 9Y = 900
∴ Y = 100 m/s = Speed of goods train
X/Y = 5/4 ⇒ Y = 4X/5
The equation (1) becomes,
X + 4X/5 = 225 ⇒ 9Y = 1125
∴ X = 125 = Speed of passenger train
On substituting value of x and y in equation (2), we get,
Z × 100/125 = 16
∴ Z = 20 hours = Time after which the trains meet
Now, the time taken to complete whole trip by passenger train is:
((20 × 100) + (20 × 125))/125 = 36 hours