Question

Will mark brainliest!!! Two trains leave towns 663 kilometers apart at the same time and travel toward each other. One train travels 19 km h slower than the other. If they meet in 3 hours, what is the rate of each train?

Answer 1

Answer: rate of train A = 120 km/h

rate of train B = 101 km/h

Step-by-step explanation:

Let x = the speed of train A

Let y = the speed of train B

One train travels 19 km/h slower than the other. Let train B be the slower train. Therefore,

x = y + 19 - - - - - - - - - -1

Recall

Speed = distance/time

Distance = speed × time

If they meet in 3 hours, it means that train A has travelled a distance of

x × 3 = 3x km

And train B has travelled a distance of y × 3 = 3y km

Train A and Train B were 663 kilometers apart when they left their respective destinations. They left at the same time and travelled towards each other. This means that if they meet in 3hours time, they must have covered a total of 663 km. Therefore,

3x + 3y = 663 - - - - - - - - - 2

Substituting x = y + 19 into equation 2, it becomes

3(y + 19) + 3y = 663

3y + 57 + 3y = 663

6y + 57 = 663

6y = 663 - 57 = 606

y = 606/6 = 101 km/h

x = y + 19 = 101 + 19

x = 120 km/h