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.  Algebra House
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