How do I find the rate of the planes

A private plane and a commercial plane take off from an airport at the same time for a city 720 miles away. The rate of the private plane is 180 miles per hour less than that of the commercial plane. If the commercial plane arrives two hours ahead of the private plane, find each plane's rate.

Let the rate of the commercial plane be x.
Then the rate of the private plane is x - 180.

Using time = distance / rate, the time it takes each plane to travel is

720/x for the commercial plane
720/(x - 180) for the private plane

If the commercial plane arrives two hours ahead of the private plane, then

720/(x - 180) - 720/x = 2

multiply both sides by x(x - 180)

720x - 720(x - 180) = 2x(x - 180)

720x - 720x + 720*180 = 2x^2 - 360x

2x^2 - 360x - 129600 = 0

x^2 - 180x - 64800 = 0

x = (180 ± √(180^2 + 4*64800))/2

x = (180 ± 540)/2

x = 360 or -180

we reject x = -180, so we get x = 360

the rate of the commercial plane is 360 mph
the rate of the private plane is 180 mph

check
the private plane reaches the city in 720/180 = 4 hours
the commercial plane reaches the city in 720/360 = 2 hours
So the commercial plane arrives two hours ahead of the private plane.

The rates are 180 and 360.

720 / r - 720 / (r + 180) = 2

720(r + 180) - 720r = 2r(r + 180)

720*180 = 2r(r + 180)

r^2 + 180r - 360*180 = 0

(r + 360)(r - 180) = 0

So the rate of the slower plane is 180 and the other rate is 180 more, or 360.