Two trans leave Chicago going opposite directions, one going north and the other going south. The northbound train is traveling 12 mph slower than the southbound train. After 4 hours the trains are 528 miles apart. Find the speed of each train. I would appreciated so much if anyone could give me directions on the question.

RT = D (Rate x Time = Distance)

R = rate of southbound train
4 = time of southbound
4R = distance of southbound train

R - 12 = rate of northbound train
4 = time of northbound
4(R - 12) = distance of northbound train

Since the sum of distances = 528
4R + 4(R - 12) = 528
Solve for R, rate of southbound train
R - 12 = rate of northbound train

Northbound train is traveling at 60 mph, the other 72.

To find the speed of each train, let's assume the speed of the southbound train is 'x' mph.

Since the northbound train is traveling 12 mph slower, its speed would be 'x - 12' mph.

Now, let's see how far each train travels in 4 hours.

The southbound train travels at 'x' mph for 4 hours, so its distance would be '4x' miles.

The northbound train travels at 'x - 12' mph for 4 hours, so its distance would be '4(x - 12)' miles.

The total distance between the two trains would be the sum of the distances traveled by each train, which we know is 528 miles:

4x + 4(x - 12) = 528

Now let's solve this equation step by step.

Expand the equation:

4x + 4x - 48 = 528

Combine like terms:

8x - 48 = 528

Add 48 to both sides of the equation:

8x = 528 + 48
8x = 576

Divide both sides of the equation by 8:

x = 576 / 8
x = 72

So, the speed of the southbound train is 72 mph.

To find the speed of the northbound train, subtract 12 from the southbound train's speed:

x - 12 = 72 - 12 = 60

Therefore, the speed of the northbound train is 60 mph.