Question 636847: The distance between train station A and train station B is 180 kilometers. Train station C is between station A and station B, and is located 30 kilometers away from station A. At 7 AM, a freight train left from station A to station B and at 8 AM, a passenger train left from station C to station B. The speed of the passenger train is 30 km/hour greater than the freight train.
The passenger train arrived to station B 20 minutes earlier than the freight train arrived to station B.
What is the speed of the freight train?
Thanks so much for your time! :)
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The distance between train station A and train station B is 180 kilometers. Train station C is between station A and station B, and is located 30 kilometers away from station A.
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Draw that picture:
30 km from A to C
180 km from A to B
150 km from C to B
A......30km.....C.............130km......B
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At 7 AM, a freight train left from station A to station B and at 8 AM, a passenger train left from station C to station B. The speed of the passenger train is 30 km/hour greater than the freight train.
The passenger train arrived to station B 20 minutes earlier than the freight train arrived to station B.
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Freight DATA:
rate = x kmh ; distance = 180 km ; time = d/r = 180/(x) hrs
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Passenger DATA:
rate = x+30 kmh ; distance = 130 km ; time = d/r = 130/(x+30) hrs
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What is the speed of the freight train?
Equation:
freight - pass = 1/3 hr
180/x - 130/(x+30) = 1/3
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3*180(x+30) - 3*130x= x(x+30)
540x + 16200 - 390x = x^2+30x
x^2 - 120x - 16200 = 0
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x = 200 kmh (freight rate)
x+30 = 230 kmh (passenger rate)
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Cheers,
Stan H.
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