1. The speed of a passenger trin is 18mph faster than the speed of a freight train. The passenger train travels 260 miles in the same time it takes the feight train to travel 170 miles. Find the speed of each train.

Answer 1

Vf = X mi/h.=Velocity of freight train.
Vp = (X + 18)mi/h = Velocity of passenger train.

Eq1: Dp = (X+18)t = 260.

Eq2: Df = Xt = 170,
t = 170/X.

In Eq1, substitute 170/X for t:
(X+18)170/X = 260,
Multiply both sides by X:
170(X+18) = 260x,
170x + 3060 = 260x,
260x - 170x = 3060,
90x = 3060,
X = 34 mi/h = Speed of freight train.
X+18 = 34 + 18 = 52 = Speed of passenger train.