[Daniel Miksch]

A car is traveling at 65 mph and passes a train in 2 minutes. A car going the opposite way passes the train in 10 seconds. How long is the train? Please explain how answer is achieved

[Clough]

Hi, Daniel Miksch!

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[Unknown008]

Is there any other information?

[ArcSine]

Just guessing... looks like maybe the missing piece is the speed of the other car. If, for example, the second car is also traveling at 65 mph, then it follows that the train's speed is 55 mph:

Letting T denote the train's speed, the first car's speed relative to the train is 65 - T. The other car's speed relative to the train is 65 + T. Both cars travel the same distance--i.e. the length of the train--but the 'same-direction' car takes 12 times as long as the 'opposite-direction' car to travel that distance; hence

65 + T = 12(65 - T)

from which the train's speed T = 55 mph follows. Thus the first car's relative (to the train) speed is 10 mph. The train's length is then the distance traveled in 2 minutes at 10 mph.

Equivalently, using the second car's relative speed as the 'yardstick', the train's length is the distance traveled in 10 seconds at 120 mph.

[Unknown008]

That's what I was trying to know, anyway, if that's the case, great answer Arcsine :)