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

Hello Chelle,

Let's call x: the rate of the slower train.

That means the rate of the faster train will be x+21

Also recall: distance = (rate)* (time)

distance traveled by slower train = x*6 = 6x

distance traveled by faster train = (x+21)*6 = 6x+126

When both trains meet, their total distance traveled will be 1506 km.

so 6x+126+6x=1506 ---> 12x + 126 = 1506 ---> 12x = 1380

From there you can:

1. solve for x, the rate of the slower train
2. Use the fact that the faster train goes 21 km/h faster than the slower train to find its rate.

Cheers.