PS - miles

[andreasonlinegr]

A certain truck traveling at 55 miles per hour gets 4.5 miles per gallon of diesel fuel consumed. Traveling at 60 miles per hour, the truck gets only 3.5 miles per gallon. On a 500-mile trip, if the truck used a total of 120 gallons of diesel fuel and traveled part of the trip at 55 miles per hour and the rest at 60miles per hour, how many miles did it travel at 55 miles per hour?

Answer: 360

[mental]

let X miles be travelled at 55mph
(500-x) miles on 60 mph

milage at 55mph = 4.5 miles per gallon
total gallon used =x/4.5 = 2x/9

milage at 60mph = 3.5 miles per gallon
total gallon used =(500 - x)/3.5 = 2(500-x)/7

2x/9 + 2(500-x)/7 = 120
Solve for x, you get 360

7x + 9(500-x) = 60*63
2x = 4500 - 3780 = 720
x=360