The speed of a passenger train is 8 mph faster than the spee

The speed of a passenger train is 8 mph faster than the speed of a freight train. The passenger train travels 260 miles in the same time it takes the freight train to travel 220 miles. Find the speed of each train.

Solution

The speed of a passenger train = 260/(x+8)
The speed of the freight train = 220/x
260/(x+8) = 220/x
Multiply each side by (x+8)(x)
260(x) = 220(x+8)
260x = 220x + 1760
260x - 220x = 220x + 1760 - 220x
40x = 1760
Divide each side by 40
x = 44
The speed of the passenger train is 52 mph and the speed of the freight train is 44 mph
check:
260/(44+8) = 220/44
260/52 = 220/44
5 = 5