SOLUTION: The rate of a passenger train exceeds the rate of a freight train by 20 mph. It takes the passenger train 1/2 as much time to travel 160 miles as it does the freight train. Find th

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Question 524011: The rate of a passenger train exceeds the rate of a freight train by 20 mph. It takes the passenger train 1/2 as much time to travel 160 miles as it does the freight train. Find the rate of each train.
Found 2 solutions by solver91311, lwsshak3:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


It doesn't make any difference how far they travel given the time and speed relationships.

Distance: distance units

Rate(speed) of freight train: distance units per time unit

Rate of passenger train: distance units per time unit

Time for freight to travel distance units: time units

Time for passenger train to travel distance units: time units

Time for freight train to go distance units at a rate of distance units per time unit:



Time for passenger train to go distance units at a rate of distance units per time unit:



Multiply the 2nd equation by 2:



Now that you have two different expressions equal to , set them equal to each other:



Cross-multiply:



Multiply both sides by





So the freight averages 20 distance units per time unit, and the passenger train goes 40 distance units per time unit. Since you were working with miles as distance unit and hours as time units, your answers should be expressed in miles per hour.

John

My calculator said it, I believe it, that settles it
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Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
The rate of a passenger train exceeds the rate of a freight train by 20 mph. It takes the passenger train 1/2 as much time to travel 160 miles as it does the freight train. Find the rate of each train.
**
let x=rate of speed of freight train
x+20=rate of speed of passenger train
Travel time=distance/rate of speed
..
160/x=2(160/(x+20)
160x+3200=320x
160x=3200
x=3200/160=20
x+20=40
ans:
rate of speed of freight train=20 mph
rate of speed of passenger train=40 mph