*50points, answer asap* one train leaves a station heading due west. two hours later a second train leaves the same station heading due east. the second train is travelling 15mph faster than the first. six hours after the train leaves, the two trains are 580 miles apart. find the rate at which each train is travelling using systems of equations.

Hello! The answer to your question would be as followed:

We have the first train going west at x speed mph

The second train is going east at (x+15) mph

The distance covered by first train in 2 hours = s · t

speed equaling x mph and time equaling 2 hours

distance = (2x) miles

Then after 2 hours, the second train leaves

After being six hours after the second train left, the two trains were 580 miles apart

Thus, eight hours after the first train left, the two trains were 580 miles apart

The distance traveled by the first train due west in 8 hours = s · t

= x · 8

= (8x) miles

The distance of the second train going east in six hours = s · t

= (x+15) · 6

Then the total distance between the trains is distance traveled by the first train added to distance traveled by the second train

8x + 6(x+15)=580

8x+6x+90=580

14x=580-90

14x=490

x=35

Meaning the first train was traveling at 35 mph

while the second train was traveling at (35+15) = 50 mph