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
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
