Look out! Two trains traveling toward each other!

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.

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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.

- Algebra House