A task about two moving trains

Question

Two trains are heading towards each other. The first train has a speed of 60 km/h, the 2nd one has the speed of 50 km/h. The length of the first train is 0.35 km, the length of the second train is 0.42 km. What is the distance between the point where the fronts of the train meet and between the point where the backs of the car meet?

I found that the closing speed of the trains is 110 km/h. Therefore, the time before the two backs met is (0.42+0.35)/110 = 0.007 h. What can I do next?

What you calculated is not the time "before the two trains meet." Think about what you actually did calculate--it is something you can use in the solution, whereas "time before the two trains meet" is both unknowable and useless to you. — David K, Mar 13 '17 at 19:26
Add assumptions, think about acceleration or friction. I believe that there should be a physics tag if so. — Xetrov, Mar 13 '17 at 20:01
It took me a moment to add the "on parallel tracks" condition! — DJohnM, Mar 13 '17 at 20:17

score 0 · Answer 1 · answered Mar 13 '17 at 19:40

0

You need to think about this a little differently ...

HINT

What would the distance be if the trains had equal length and speed?

How would this change if they had equal speed but different length?

And what about equal length but different speed?

answered Mar 13 '17 at 19:40

Bram28

100,612
6
70
118

score 0 · Answer 2 · answered Mar 13 '17 at 20:19

The problem is actually easier than it sounds.

You have done the hard part, which is to figure out the amount of time that passes from the instant when the fronts of the train meet until the instant when the backs of the trains meet.

Now suppose that at the instant when the fronts of the trains meet, we plant a flag in the ground alongside the tracks at the place where that event occurred, and a little later, when the backs of the trains meet, we plant another flag in the ground alongside the tracks at the place where that event occurred. The question is asking about the distance between the flags.

At the instant you plant the first flag, the front of each train is also at that point along the tracks. You know how far away the back of the first train is at that time, how fast it is moving toward you, and how much time elapses until you must plant the second flag. Now use that information to figure out where the back of the first train is when you plant the second flag, and that will tell you where the second flag will be.

You can check your work by using the information you have about the second train to figure out where the back of that train will be at the instant the second flag is planted. It should be at the same point!

I've noticed that the the distance which the first back passed equals the length of the second train and vice versa. What now? — student28, Mar 13 '17 at 20:20
@student28 Yes, I see that. It's a cute coincidence, but not actually necessary for the solution of the problem. The problem would also have a solution if the lengths of the trains were $0.3$ and $0.47,$ everything else being the same, but of course the number in the answer would be different. — David K, Mar 13 '17 at 20:24
So the location of the flag is 0.007h60 km/h -0.35 = 0.07 km = 70m, which equals |0.00750-0.42|, so the answer is 70 metres, right? — student28, Mar 13 '17 at 20:26

A task about two moving trains

2 Answers2