Question

Options for the first box: Time it takes Gilbert to travel 5 miles, increase in Gilberts average biking speed, distance Gilbert travels, biking speed for the second practice rideOptions for the second box: add, multiply, divide, subtract

Answer 1

We know that Gilbert's first practice ride covers 5 miles of the course, and his second practice ride covers 9 miles of the course.

And we also know that between these practice rides, he increase his average speed by 2 miles/hour.

We have the next two functions:

- First practice ride :

`a(x)=(5)/(x)`

- Second practice ride :

`b(x)=(9)/(x+2)`

Where, x represents his speed during the first practice ride

a) We know that

`velocity=\frac{distance}{\text{time}}`

So, if the functions model the time

`\text{time}=\frac{\text{distance}}{\text{velocity}}`

We can see that the denominator represents the velocity.

Finally, the denominator of the function that models practice ride 2 represent the biking speed for the second practice ride.

b) Knowing that a(x) and b(x) represent the time it took Gilbert to do each practice ride,

to find the a function that models the total amount of time Gilbert spent doing practice rides on the race course, add the functions.