Question 912225: An empty freight train traveled 60 miles from an auto assembly plant to an oil refinery. There, its tank cars were filled with petroleum products, and it returned on the same route to the plant. The total travel time for the train was 5 1/2 hours. If the train traveled 25 mph slower with the tank cars full, how fast did the train travel in each direction?
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! An empty freight train traveled 60 miles from an auto assembly plant to an oil refinery. There, its tank cars were filled with petroleum products, and it returned on the same route to the plant. The total travel time for the train was 5 1/2 hours. If the train traveled 25 mph slower with the tank cars full, how fast did the train travel in each direction?
An empty freight train traveled 60 miles from an auto assembly plant to an oil refinery.
let x mph be the speed when empty
train traveled 25 mph slower with the tank cars full (x-25) mph
The total travel time for the train was 5 1/2 hours.
Time forward + time return = 5.5 hours
t=d/r
60/x +60/(x-25) = 5.5
multiply equation by LCM x(x-25)
60(x-25)+60x = 5.5x(x-25)
60x-1500+60x= 5.5x^2-137.5x
*2
120x-3000+120x=11x^2-275x
11x^2-515x+3000=0
solve the quadratic equation
x= 40 mph
check
60/40 + 60/(40-25)
3/2 + 4= 5.5
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