SOLUTION: A passenger train leaves a train depot 2 h after a freight train leaves the same depot. The freight train is traveling 20 mph slower than the passenger train. Find the rate of each

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Question 1152267: A passenger train leaves a train depot 2 h after a freight train leaves the same depot. The freight train is traveling 20 mph slower than the passenger train. Find the rate of each train if the passenger train overtakes the freight train in 3 h.
Found 3 solutions by josmiceli, greenestamps, MathTherapy:
Answer by josmiceli(19441) About Me  (Show Source):
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Let +s+ = the speed of the passenger train in mi/hr
+s+-+20+ = the speed of the freight train
+%28+s+-+20+%29%2A2+ = the distance of the freight train's head start
Let +d+ = distance the passenger train travels in 3 hrs
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Equation for the passenger train:
(1) +d+=+s%2A3+
Equation for the freight train:
(2) +d+-+%28+s+-+20+%29%2A2+=+%28+s+-+20+%29%2A3+
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Plug (1) into (2)
(2) +3s+-+%28+s+-+20+%29%2A2+=+%28+s+-+20+%29%2A3+
(2) +3s+-+2s+%2B+40+=+3s+-+60+
(2) +2s+=+100+
(2) +s+=+50+
and
+s+-+20+=+30+
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The rate of the passenger train is 50 mi/hr
The rate of the freight train is 30 mi/hr
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check:
(1) +d+=+s%2A3+
(1) +d+=+50%2A3+
(1) +d+=+150+ mi
and
(2) +d+-+%28+s+-+20+%29%2A2+=+%28+s+-+20+%29%2A3+
(2) +d+-+30%2A2+=+30%2A3+
(2) +d+=+60+=+90+
(2) +d+=+150+
and
The head start for freight train is:
+d%5B1%5D+=+30%2A2+
+d%5B1%5D+=+60+
---------------------
The time for the remaining 90 miles is:
+t+=+90%2F30+
+t+=+3+ hrs
OK
get a 2nd opinion if you need to

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 that the freight train covers in 5 hours. The ratio of times for the same distance is 3:5, so the ratio of their speeds is 5:3.

If x is the speed of the freight train, then the speed of the passenger train is x+20. Since the ratio of the speeds is 5:3,

%28x%2B20%29%2Fx+=+5%2F3
5x+=+3x%2B60
2x+=+60
x+=+30

The speed of the freight train is x=30mph; the speed of the passenger train is x+20=50mph.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

A passenger train leaves a train depot 2 h after a freight train leaves the same depot. The freight train is traveling 20 mph slower than the passenger train. Find the rate of each train if the passenger train overtakes the freight train in 3 h.
Let the speed of the passenger train be S

Then the speed of the freight train = S - 20

We then get the following DISTANCE equation: 3S = (2 + 3)(S - 20)_____3S = 5S - 100

3S - 5S = - 100

S, or 

Speed of freight train: highlight_green%28matrix%281%2C4%2C+50+-+20%2C+%22=%22%2C+30%2C+mph%29%29