SOLUTION: A passenger train leaves a depot 1.5 h after a freight train leaves the same depot. The passenger train is traveling 18 mph faster than the freight train. Find the rate of each tra

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Question 948523: A passenger train leaves a depot 1.5 h after a freight train leaves the same depot. The passenger train is traveling 18 mph faster than the freight train. Find the rate of each train if the passenger train overtakes the freight train in 2.5 h
Answer by Stitch(470) About Me  (Show Source):
You can put this solution on YOUR website!
Speed is distance traveled over time.
Or S+=+D%2FT
We can rewrite the equation to solve for distance by multiplying both sides by T
S%2AT+=+D
Let F = Speed of the freight train
Let P = Speed of the passenger train
Let Tf = Time for freight train.
Let Tp = Time for passenger train
Tf = 2.5 hours
Tp = 2.5 - 1.5 = 1 hour
We can now write three equations.
Equation 1: P+=+F+%2B+18
Equation 2: F%2ATf+=+D
Equation 3: P+%2A+Tp+=+D
When the passenger train overtake the freight train the distance traveled will be the same. So the D's in equations 2 and 3 will be the same so we can set those two equations equal to each other.
F%2ATf+=+P%2ATp
Plug in the given values for the variables.
F%2A2.5+=+P%2A1
Now look at equation 1. We know that P = F+18. Plug that into our equation.
F%2A2.5+=+%28F%2B18%29%2A1
Simplify
2.5%2AF+=+F%2B18}
Subtract 1F from both sides.
1.5%2AF+=+18
Divide both sides by 1.5
highlight%28F+=+12%29
The freight train is traveling at 12mph.
Now plug 12 into equation 1 for F
Equation 1: P+=+F+%2B+18
P+=+%2812%29+%2B+18
highlight_green%28P+=+30%29
The passenger train is traveling at 30mph