Question 488023: How do I solve the following:
A freight train leaves the train station 2 hours before a passenger train. The two trains are traveling in the same direction on parallel tracks. If the rate of the passenger train is 20 mph faster than the frieght train, how fast is each train traveling if the passenger train passes the freight train in 3 hours.
Found 2 solutions by stanbon, Edwin McCravy:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A freight train leaves the train station 2 hours before a passenger train.
The two trains are traveling in the same direction on parallel tracks.
If the rate of the passenger train is 20 mph faster than the frieght train, how fast is each train traveling if the passenger train passes the freight train in 3 hours.
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Freight train DATA:
time = 3+2 hrs ; rate = r mph ; distance = r(5) miles
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Passenger train DATA:
time = 3 hrs ; rate = r+20 mph ; distance = 3(r+20) miles
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Equation:
distance = distance
5r = 3r+60
2r = 60
r = 30 mph (freight train rate)
r+20 = 50 mph (passenger train rate)
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Cheers,
Stan H.
Answer by Edwin McCravy(20054)  (Show Source):
You can put this solution on YOUR website! A freight train leaves the train station 2 hours before a passenger train. The two trains are traveling in the same direction on parallel tracks. If the rate of the passenger train is 20 mph faster than the frieght train, how fast is each train traveling if the passenger train passes the freight train in 3 hours.
It is not clear whether you mean 3 hours after the freight train passes
the station or 3 hours after the passenger train passes the station. I
will assume you mean 3 hours after the passenger train reaches the station.
Let the speed of the freight train be x. Then 2 hours later when the
passenger train gets to the station, since distance = (rate)(time),
the freight train is 2x miles up the track from the station. That is,
the distance between them when the passenger train is at the station,
is 2x miles, which means the freight train has a 2x mile head start.
The approach rate of the passenger to the freight is 20 mph.
If the 3 hours is from the time the passenger train gets to the station,
then since
distance to catch up = approach rate × time
2x = 20(3)
2x = 60
x = 30
So the freight train is going 30 mph and the passenger train is
going 20 mph faster or 50 mph.
Checking. Suppose the freight train leaves the station at 12:00 noon.
That's 2 hours before the passenger train gets to the station.
So the passenger train is 100 miles from the station. The passenger
train gets to the station at 2PM, and by then, the freight train is 60
miles up the track. 3 hours later at 5PM the freight train has gone an
additional 90 miles so it is 150 miles from the station. In those same
3 hours from 2PM till 5PM, the passenger train has also gone 150 miles
from the station, so it has caught up to the freight train at 5PM 150
miles from the station. So we are correct.
Edwin
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