Two airplanes leave the airport at the same time, traveling in opposite directions. One plane travels 30 mph faster than the other. After 3 hours, the planes are 3150 miles apart. What is the rate of each plane?

Let x mph and x+30 mph be the speeds of the planes. The rate at which their distance from each other increases will be the sum of their speeds which is 2x+30 mph.

Their distance from each other after three hours is (3 hours)*(2x+30 mph) = 6x+90 miles. We are given that this is 3150 miles so we can solve for x.

6x+90 = 3150

6x = 3060

x = 510

Thus the speeds of the two planes are 510 mph and 540 mph.