Two high speed trains are 240 miles apart and traveling toward each other. They meet in 2 hours. If one trains speed is 10 miles per hour faster than the other, find the speed of each train.

**Distance = rate x time**

Rate of one train = r

Time of one train = 2 hours

Distance of one train = 2r {distance = rate x time}

Rate of other train = r + 10 {it is 10mph faster than the other one}

Time of other train = 2 hours

Distance of other train = 2(r + 10) = 2r + 20 {distance = rate x time with distributive property}

2r + 2r + 20 = 240 {the combined distances of the two trains is 240}

4r + 20 = 240 {combined like terms}

4r = 220 {subtracted 20 from each side}

r = 55 mph rate of one train {divided each side by 4}

r + 10 = 65 mph rate of other train {substituted 55, in for r, into r + 10}

**The rate of one train is 55 mph.**

The rate of the other train is 65 mph.

The rate of the other train is 65 mph.

*- Algebra House*