Two trains leave towns 492 miles apart at the same time and travel toward each other. One train travels 16 miles per hour slower than the other. If they meet in 3 hours, what is the rate of each train?

The rate of each train is 74 miles per hour and 90 miles per hour respectively.

Step-by-step explanation:

Given;

distance between the two trains, d = 492 miles

total time traveled by each train before meeting the other, t = 3 hours

Let the speed for the first train = p

Let the speed for the second train = q

Assuming the first train is 16 mph slower than the second train, then;

q = p + 16

Distance = speed x time

492 miles = (p + q) x 3

492 = 3p + 3q

but, q = p + 16

492 = 3p + 3 (p + 16)

492 = 3p + 3p + 48

492 - 48 = 6p

444 = 6p

p = 444 / 6

p = 74 miles per hour

q = 74 + 16

q = 90 miles per hour

Therefore, the rate of each train is 74 miles per hour and 90 miles per hour respectively.