the first 50 miles of the drive is easy, while the last 68 miles of the drive is filled with curves. they drive at an average of 9 miles per hour faster for the first 50 miles of the trip. the entire trip takes 3 hours. how fast did they drive for the first 50 miles of the trip?

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