SOLUTION: A freight train leaves a station and travels east at an average speed of 48 mph. Later, a passenger train leaves the same station on parallel tracks and follows the freight train

Question 1093875: A freight train leaves a station and travels east at an average speed of 48 mph. Later, a passenger train leaves the same station on parallel tracks and follows the freight train at an average speed of 60 mpg. If the passenger train overtakes the freight in 2 hours, how much of a head start did the freight train have?
Found 2 solutions by stanbon, greenestamps:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A freight train leaves a station and travels east at an average speed of 48 mph. Later, a passenger train leaves the same station on parallel tracks and follows the freight train at an average speed of 60 mpg. If the passenger train overtakes the freight in 2 hours, how much of a head start did the freight train have?
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Freight train DATA:
rate = 48 ; time = x hrs ; distance = r*t = 48x miles
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Passenger train DATA:
rate = 60 mph ; time = 2 hrs ; distance = 60*2 = 120 miles
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Distances are the same::
48x = 120
x = 2.5 hrs
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Head start = freight time - passenger time = 2.5-2 = 1/2 hour
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Cheers,
Stan H.
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Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

Each hour, the passenger train goes 12 miles farther than the freight train.

If it catches up to the freight train in 2 hours, then it went 24 miles farther than the freight train; in other words, the freight train was 24 miles from the station when the passenger train started.

If the freight train, traveling at 48mph, was 24 miles from the station when the passenger train started, then it must have started 1/2 hour before the passenger train.
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