.
Notice that when the diesel train started, the freight train was 55 miles ahead.
But the diesel train, having the speed in 5 = 60-55 miles per hour greater than the freight train,
will decrease the distance between them by 5 miles each hour.
So, it will take 11 hours ( where 
) for the diesel train to catch the freight train.
Correspondingly, it will take 12 = 11+1 hours for the freight train to get the meeting point.
It is how the physicists solve such problem.
Below find the way on how this problem is solved in Algebra.
Let t = "How long did the freight train travel before the diesel train caught up", in hours (the value under the question).
Then the diesel train traveled (t-1) hour.
They both covered the same distance:
60*(t-1) = 55*t
60t - 60 = 55t
60t - 55t = 60 ====> t = 
= 12 hours.
Solved (in two different ways).
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See introductory lessons on Travel and Distance problems
- Travel and Distance problems
- Travel and Distance problems for two bodies moving in opposite directions
- Travel and Distance problems for two bodies moving in the same direction (catching up)
in this site.
They are written specially for you.
You will find the solutions of many similar problems there.
Read them and learn once for all from these lessons on how to solve simple Travel and Distance problems.
Become an expert in this area.
