SOLUTION: A freight train travels north at a rate of 50mph. A passenger train leaves 4 hours later on a parallel track and travels north at 90mph. How long will it take the passenger train t

Question 1091996: A freight train travels north at a rate of 50mph. A passenger train leaves 4 hours later on a parallel track and travels north at 90mph. How long will it take the passenger train to catch up to the freight train?
Found 3 solutions by josmiceli, ikleyn, greenestamps:
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
The head start of the freight train in miles is:

mi
---------------------
Start a stopwatch when the passenger train leaves.
Let = time in hrs on the stopwatch when the
passenger train catches up with the freight train
Let = distance in miles the passenger train
travels until it catches up with the freight train
-----------------------------------------------
Equation for the pasenger train:
(1)
Equation for the freight train:
(2)
---------------------------------
Plug (1) into (2)
(2)
(2)
(2)
The passenger train will catch the freight train in 5 hrs
----------------------
check:
(1)
(1)
and
(2)
(2)
(2)
OK
Answer by ikleyn(52772)   (Show Source): You can put this solution on YOUR website!
.
For two bodies moving in the same direction (catching up problems) see the lesson
    - Travel and Distance problems for two bodies moving in the same direction (catching up)
in this site.

Actually, there are 3 methods of solving this kind of problems: - using two "time - distance" equations, - using one "time - distance" equation, and - MENTAL solution without using equations. In the referred lesson you will find the descriptions and examples of solved problems for all three approaches.

When you complete reading this lesson - let me know by sending the message through the "Thank you" window,
referring to the ID number of the current problem, which is 1091996.

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Answer by greenestamps(13198)   (Show Source): You can put this solution on YOUR website!

In the 4 hours that the first train travels before the second train starts, the first train travels 4*50 = 200 miles.

The second train travels 40mph faster than the first train (90 minus 50).

The number of hours the second train needs to overtake the first train is the number of hours it needs to make up 200 miles, when it does so at a rate of 40 miles each hour:

It takes the second train 5 hours to overtake the first.
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