let

m = the speed of Mattie

d1 = 180 mi the distance Mattie traveled

p = the speed of the plane

d2 = 630 mi the distance the plane traveled

the speed of the plane was 150 mph faster than the speed of the car

p = m + 150

since speed = distance/time => time = distance/speed

d1/m = d2/p

180/m = 630/p cross multiply

180p = 630m divide both sides by 90

2p = 7m

by solving the system of equations

p = m + 150

2p = 7m

we find

p = 210 mph

click here to see the step by step solution of the system of equations

the speed of the plane was 210 mph.