Let x represent the rate of the slower plane. If this slower plane travel 77 km/h slower than the faster plane, it means that the rate of the faster plane is
x + 77
Recall, distance travelled = speed * time
Given that both planes travelled for 7 hours,
Distance travelled by slower plane = 7 * x = 7x
Distance travelled by faster plane = 7(x + 77) = 7x + 539
If both planes are 12,859 km apart after seven hours, it means that the total distance travelled by both planes after 7 hours is
7x + 7x + 539 = 12859
14x+ 539 = 12859
14x = 12859 - 539 = 12320
x = 12320/14 = 880
Thus,
Rate of slower plane = 880 km/h
Rate of faster plane = 880 + 77 = 957 km/h