Call the speed of the express v. Then the speed of the bus is v - 7 (mph).
Call the time it takes the express to travel 90 miles t. Then it also takes the bus a time t to travel 75 miles. Since d = vt:
90 mi = vt (Express)
75 mi = (v - 7)t (Bus)
(I'll drop the units until the end for convenience.)
So from the first equation:
t = 90/v
Insert this into the second equation:
75 = (v - 7)*(90/v) <-- Multiply both sides by v:
75v = 90v - 630
15v = 630
v = 42 mph
v - 7 = 35 mph.