SOLUTION: Train Speed: A train leaves Los Angeles at 2:00 PM. A second train leaves the same station in the same direction at 4:00 PM. The second train travels 24 mph faster than the first.

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Question 648831: Train Speed: A train leaves Los Angeles at 2:00 PM. A second train leaves the same station in the same direction at 4:00 PM. The second train travels 24 mph faster than the first. If the second train overtakes the first at 7:00 PM, what is the speed of each of the two trains?
I am not sure how to construct an equation to solve this problem.
Thanks for your help!
Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website!
Let the speed of the 1st train =
= the speed of the 2nd train
Let = the head start that the 1st train got
4 PM - 2PM is hrs, so

Let = the distance that the 2nd train has to go
to catch the 1st train
----------------
7PM - 4PM = hrs
Use this time for both trains. Figure that
the 1st train already has the head start
-----------------
1st train's equation:

(1)
-----------------
2nd train's equation:
(2)
----------------------
(1)
and
(2)
------------------
Substitute (1) into (2)
(2)
(2)
(2)
also

---------------
The 1st train's speed is 36 mi/hr
The 2nd train's speed is 60 mi/hr
check:

So, the 1st train had a head start of 72 mi
which took 2 hrs. Now it has 3 hrs to go
the rest of the way
2nd train's equation:
(2)
(2)
(2) mi
mi
The 1st train must go 108 mi in 3 hrs at 36 mi/hr

OK