I don't understand the reasoning behind a few steps in this problem:

What constant acceleration is required to increase the speed of a car from 30 mi to 50 mi in 5 seconds?

a(t) = C = v'(t)

v'(t) = Ct + K

v(0)=30= C(0) + k

k = 44 ?

v(5) = (5/6)88 ft/s ?

v(5) = 5c + 44

5c = 88/3 = 88/15 ft/s^2

I think I know where k = 44 comes from.

50 mi - 30mi = 20mi

20mi/5s = 4mi/s(30mi) = 120mi/s

5280/120 = 44

But I don't understand where the other number comes from.