For first 50 miles:-
x + 9 = 50 / t where x is average speed for the last 68 miles and t = time taken for the first 50 miles.
For the second 68 miles:-
x = 68 / (3 - t)
Substitute for x in first equation:-
68 / (3 - t) + 9 = 50/t
68t + 9t(3 - t) = 50(3 - t)
68t + 27t - 9t^2 = 150 - 50t
9t^2 - 145t + 150 = 0
t = 1.111 , 15 (ignore the 15 hours as total time = 3).
so the speed for the first 50 miles = 50 / 1.111 = 45 miles per hour Answer
