SOLUTION: A passenger train leaves a train depot 2 h after a freight train leaves the same depot. The freight train is traveling 28 mph slower than the passenger train. Find the rate of each

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Question 1158476: A passenger train leaves a train depot 2 h after a freight train leaves the same depot. The freight train is traveling 28 mph slower than the passenger train. Find the rate of each train if the passenger train overtakes the freight train in 3 h.
Found 2 solutions by josmiceli, greenestamps:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = the speed of the passenger train in mi/hr
+s+-+28+ = the sped of the freight train in mi/hr
Let +d+ = the distance from depot to where they meet
Start a stopwatch when the passenger train leaves
The freight train's head start is
+d%5B1%5D+=+%28+s+-+28+%29%2A2+
+d%5B1%5D+=+2s+-+56+
----------------------------
Equation for the passenger train:
(1) +d+=+s%2A3+
Equation for the freight train:
(2) +d+-+d%5B1%5D+=+%28+s+-+28+%29%2A3+
---------------------------------------
(2) +d+-+%28+2s+-+56+%29+=+%28+s+-+28+%29%2A3+
Plug (1) into (2)
(2) +3s+-+%28+2s+-+56+%29+=+%28+s+-+28+%29%2A3+
(2) +3s+-+2s+%2B+56+=+3s+-+84+
(2) +2s+=+140+
(2) +s+=+70+
and
+s+-+28+=+42+
-------------------------
The speed of the passenger train is 70 mi/hr
The speed of the freight train is 42 mi/hr
-------------------------------------------------
check:
(1) +d+=+s%2A3+
(1) +d+=+70%2A3+
(1) +d+=+210+
and
(2) +d+-+d%5B1%5D+=+%28+s+-+28+%29%2A3+
(2) +d+-+%282s+-+56%29+=+%28+s+-+28+%29%2A3+
(2) +d+-+2%2A70+%2B+56+=+42%2A3+
(2) +d+-+140+%2B+56+=+126+
(2) +d+-+140+%2B+126+-+56+
(2) +d+=+210+
OK

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The passenger train covers in 3 hours the same distance the freight train covers in 5 hours, so the ratio of the speeds is 5:3.

Let the two speeds be 5x for the passenger train and 3x for the freight train (a standard step, given that the ratio is 5:3).

The difference in their speeds is then 5x-3x=2x.

But we know the difference in the speeds is 28 mph. So

2x = 28
x = 14

The speed of the freight train is 3x = 42 mph; the speed of the passenger train is 5x = 70 mph.