What is the sum of the lengths of two trains that will protrude from the tunnels at the exact moment that they collide?

Question

Two trains, each two miles long, enter two one mile long tunnels that are two miles apart from one another on the same track. The trains enter the tunnels at exactly the same time. The first train is going 5 miles/hour, and the second train is going 10 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

2/3 miles

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Distance between trains- 2+1+1=4 miles
Effective speed- 5+10=15 miles/hr
Time to collision- 4/15 hr
First trains travel before collision- 5*4/15=4/3 miles
Second trains travel- 10*4/15=8/3 miles
As the first train travels the distance less than it's length- 2-4/3= 2/3 miles will prorude
Second train travels more than it's lengths so no protrusion. So total length to protrude is 2/3 miles

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