Gilbert is training for a bike race. As part of his training, he does practice rides on portions of the actual race course. Gilbert’s first practice ride covers 5 miles of the course, and his second practice ride covers 9 miles of the course. Between these practice rides, he increases his average speed by 2 miles/hour. These functions model the time it took Gilbert to do each practice ride, where x is his speed during the first practice ride.

Practice Ride 1 Practice Ride 2

a(x) = 5/x b(x) = 9/ x+2

The denominator of the function that models practice ride 2 represents the

.

To find a function that models the total amount of time Gilbert spent doing practice rides on the race course,

the functions.