Math questions algebra

Question

Two planes start from the same point and fly in opposite directions. The first plane is flying 15 mph slower than the second plane. In 2 h, the planes are 450 mi apart. Find the rate of each plane.

Answer 1

Let r = the rate of the first plane and r+15 be the rate of the second plane. Since they are flying in opposite directions, their distances over time will accumulate.

After 2 hours:

2r + 2(r+15) = 450

4r + 30 = 450

r = 420/4 = 105

r+15 = 120

The first plane is flying at 105 mph and the second plane is flying at 120 mph.