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

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Question 835581: A passenger train leaves a depot 1.5 h after a freight train leaves the same depot. The passenger train is traveling 18mph faster than the freight train. Find the rate of each train if the passenger train overtakes the freight train in 2.5h.
Found 2 solutions by stanbon, josgarithmetic:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
A passenger train leaves a depot 1.5 h after a freight train leaves the same depot. The passenger train is traveling 18mph faster than the freight train. Find the rate of each train if the passenger train overtakes the freight train in 2.5h.
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Freight train DATA:
rate = r mph ; time = 4 hr ; distance = 4r miles
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Passenger train DATA:
rate = r+18 mph ; time = 2.5 hr distance = 2.5(r+18) miles
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Equation:
distance = distance
4r = 2.5(r+18)
4r = 2.5r + 45
1.5r = 45
r = 30 mph (freight rate)
r + 18 mph (passenger rate)
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Cheers,
Stan H.
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Answer by josgarithmetic(39625) (Show Source):
You can put this solution on YOUR website!
______________speed__________time__________distance
passenger_____r+18___________t-1.5_________d
freight________r______________t____________d

t = unknown, but quickly solvable.
r = unknown
hours, according to description.
hours, so t is now known.

Revise data table:
______________speed__________time__________distance___Equations
passenger_____r+18___________4-1.5=2.5_________d______
freight________r______________4____________d__________

Two different expressions for d are equal.
Solve for r.