let

x = the speed of the first plane

y = the speed of the second plane

d = 1620 miles

t = 1.5 hours

one plane is traveling 8 mph faster than the other plane

x = y + 5

since the speed = distance/time => distance = speed*time

distance the first plane crossed + the distance second plane crossed = the distance between them

x*t + y*t = d

1.5*x + 1.5*y = 1620

by solving the system of equations

x = y + 5

1.5*x + 1.5*y = 1620

we find

x = 542.5 mph

y = 537.5 mph

the speeds of the planes are 542.5 mph and 537.5 mph.