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

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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) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = the speed of the 1st train in mi/hr
+s+%2B+20+ = the speed of the 2nd train in mi/hr
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What is the 1st train's head start in miles?
+d%5B1%5D+=+s%2A2+
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Start a stopwatch when the 2nd train leaves
at 3 PM and stop the stopwatch at 9 PM
Let +d+ = distance in miles the 2nd train
travels until it catches up with 1st train at 9 PM
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Equation for 1st train:
(1) +d+-+2s+=+s%2A6+
Equation for 2nd train:
(2) +d=+%28+s%2B20+%29%2A6+
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Substitute (2) into (1)
(1) +%28+s%2B20+%29%2A6+-+2s+=+s%2A6+
(1) +6s+%2B+120+-+2s+=+6s+
(1) +2s+=+120+
(1) +s+=+60+
and
+s+%2B+20+=+80+
The 1st train's speed is 60 mi/hr
The 2nd train's speed is 80 mi/hr
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check:
(1) +d+-+2s+=+s%2A6+
(1) +d+-+2%2A60+=+6%2A60+
(1) +d+-+120+=+360+
(1) +d+=+480+
and
(2) +d+=+%28+s%2B20+%29%2A6+
(2) +d+=+%28+60%2B20+%29%2A6+
(2) +d+=+80%2A6+
(2) +d+=+480+
OK