SOLUTION: A train leaves Philadelphia at 1:00 PM. A second train leaves the same city in the same direction at 3:00 PM. The second train travels 20 mph faster than the first. If the second t

Question 1032342: A train leaves Philadelphia at 1:00 PM. A second train leaves the same city in the same direction at 3:00 PM. The second train travels 20 mph faster than the first. If the second train overtakes the first at 9:00 PM, what is the speed of each of the two trains?
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = the speed of the 1st train in mi/hr
= the speed of the 2nd train in mi/hr
-------------------------
What is the 1st train's head start in miles?

----------------
Start a stopwatch when the 2nd train leaves
at 3 PM and stop the stopwatch at 9 PM
Let = distance in miles the 2nd train
travels until it catches up with 1st train at 9 PM
----------------
Equation for 1st train:
(1)
Equation for 2nd train:
(2)
----------------------
Substitute (2) into (1)
(1)
(1)
(1)
(1)
and

The 1st train's speed is 60 mi/hr
The 2nd train's speed is 80 mi/hr
------------------------------
check:
(1)
(1)
(1)
(1)
and
(2)
(2)
(2)
(2)
OK
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