Can anyone help me on this really tough math problem?

Question

Okay this really tough math problem is getting to me!! My friend gave me the word problem saying it's quit simple. But I can't seem to find it that way!! If any one thinks they might be able to figure it out here it is:
Two trains, each three miles long, enter seven one mile long tunnels that are five miles apart from one another on the same track. The trains enter the tunnels at exactly the same time. The first train is going 7 miles/hour, and the second train is going 16 miles/hour. What is the sum of the lengths of the two trains that will protrude from the tunnels at the exact moment that they collide, assuming that neither train changes its speed prior to collision? The trains are on the same track headed in opposite directions (i.e. directly toward one another).

Answer 1

I'm right. Intel_knight miscalculated.

5 miles.

It is somewhat obvious if you leave out the info you don't need. It doesn't matter how fast the trains are going.

The sum of the length of the two trains is 6 miles. The tunnels are 1 mile long and 5 miles apart. Anywhere in the middle of the track, 6 miles of the track will have 1 mile of tunnel and 5 miles of no tunnel.

***to Intel_Knight: at the moment the trains enter the first tunnel, they will be 37 miles apart not 7 (7 1-mile tunnels + 6 5-mile gaps inbetween) but like I said, it doesn't matter anyway. Also, you are told to add the lengths of the train that protrude from a tunnel, which is the tail AND the head.

let's assume that your calculations are right (which I don't think they are, but again, it doesn't matter).

You said the head of the first train will stick out 1.33 miles out of the tunnel. But the tunnel is only 1 mile long. Since the train is 3 miles long, the head of the first train will stick out 1.33 miles out of the tunnel, then a mile of tunnel, AND the .67 miles of the tail of the first train will be sticking out the other end.

You also said that the entire 3 miles of 2nd train are out.

so the total is 1.33 + (.67) +3 = 5 miles <<< answer******

Answer 2

q_midori is wrong - 2nd train will leave the tunnel completely.

at the beginning, heads of trains are 7 miles apart (1+5+1), and they move towards each other at 16+7=23 mph
so they will collide in 7/23 ~ 1/3 hour (=20 minutes)

at the beginning, tails of trains are 3 miles outside the tunnel.
Before the collision, 1st train will travel 7*1/3 = 2.33 miles, so the head will stick out 1.33 miles out of the tunnel.

2nd train will travel 16/3 = 5.33 miles, which puts the tail 1.33 miles out of the tunnel (5.33-3-1), so entire 3 miles of 2nd trail are out.

so the total is 1.33+3 = 4.33 miles <<< answer

If you want more precision, use actual 7/23 instead of 1/3

So out of 5 miles between tunnels, only 1.33 mile will be free of trains, and 5-1.33=3.67 will be com