SOLUTION: A train leaves Orlando at 1:00 PM. A second train leaves the same city in the same direction at 3:00 PM. The second train travels 32 mph faster than the first. If the second tra

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Question 950545: A train leaves Orlando at 1:00 PM. A second train leaves the same city in the same direction at 3:00 PM. The second train travels 32 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?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = the speed in mi/hr of the 1st train
+s+%2B+32+ = the speed in mi/hr of the 2nd train
--------------------
From 1 PM to 3 PM is +2+ hrs
The 1st train's head start is:
+d%5B1%5D+=+s%2A2+
--------------------
Start a stopwatch when the 2nd train leaves
at 3 PM and stop the watch at 7 PM
--------------------
Let +d+ = the distance the 2nd train travels
from 3 PM to 7 PM
--------------------
Equation for the 1st train:
(1) +d+-+d%5B1%5D+=+s%2A4+
Equation for the 2nd train:
(2) +d+=+%28+s%2B32+%29%2A4+
---------------------
(1) +d+-+2s+=+4s+
(1) +d+=+6s+
Plug this result into (2)
(2) +6s+=+%28+s+%2B+32+%29%2A4+
(2) +6s+=+4s+%2B+128+
(2) +2s+=+128+
(2) +s+=+64+
and
+s+%2B+32+=+96+
------------------
The speed of the 1st train is 64 mi/hr
The speed of the 2nd train is 96 mi/hr
check:
(1) +d+=+6s+
(1) +d+=+6%2A64+
(1) +d+=+384+
and
(2) +d+=+%28+s%2B32+%29%2A4+
(2) +d+=+96%2A4+
(2) +d+=+384+
OK