Question

Two trains are 360 miles apart at 7 a.m. and are traveling on the same track, in opposite directions, moving toward one another. One train is traveling at 40 miles per hour and the other is traveling at 50 miles per hour. At what time will they meet?

Answer 1

at 4 hours after leaving, that is at 11 am

Explanation:

1) finding the distance of the meeting point (X):

so for the train 1, the distance is "X"; for the train 2, the distance would be "360 - X"

2) replacing in the ecuation: V = X / t:

train 1: 40 miles/h = (360 - X) / t.....(1)

train 2: 50 miles/h = X / t......(2)

⇒ from (2): t = X / 50..... (3)

replacing (3) in (1):

⇒ 40 = (360 - X) / ( X / 50)

⇒ 40 = (50 * (360 -X)) / X

⇒ 40X = 18000 - 50X

⇒ 90X = 18000

⇒X = 18000 / 90 = 200 miles .....meeting distance (4)

replacing (4) in (2):

⇒50millas/h = (200miles) / t

⇒ t = 200miles / 50 miles/h

⇒ t = 4h