Math help: LINES, FUNCTIONS, SYSTEMS Solving a distance, rate, time problem using a system of linear equations

Question

Two trains leave towns 1506 kilometers apart at the same time and travel toward each other. One train travels 21km faster than the other. If they meet in 6 hours, what is the rate of each train?

Answer 1

x= 21+ y = speed of the faster train, y= speed of the slower train

distance = rate of speed times time, d=rt

1506 =6(x+y)

1506 = 6(y+21+y)

1506/6 = 2y +21

2y = 251-21 = 230

y = 230/2 = 115 kph = speed of the slower train

x = 115+21 = 136 kph = speed of the faster train

in 6 hours the slower train goes 6(115) = 690 km

in 6 hours the faster train goes 6(136) = 816 km

690+816 = 1506 km