Laura will go for a run during her lunch break if the temperature is between 60∘F

80∘F. The average speed, S, in miles per hour, at which Laura runs is dependent on the temperature, t, in degrees Fahrenheit (F) ∘, at the start of her run and can be modeled by the function S (t) = 6+0.1 (80-t). The distance, D, in miles, that she can run in 30 minutes given that her average speed is x miles per hour can be modeled by the function

D (x) = 0.5x

Find an explicit expression that models the distance that Laura runs in 30 minutes given that it is t∘F outside at the start of her run.

D (t) = 3 + 0.0 (80 - t)

Step-by-step explanation:

The average of speed of Laura in miles per hour is given by:

S (t) = 6 + 0.1 (80 - t) Equation 1

where, t is the temperature in degrees Fahrenheit.

The distance D, Laura covers at x miles per hour is given as:

D (x) = 0.5x Equation 2

We need to find the expression that models the distance that Laura runs in terms of the temperature "t"

The "x" in Equation 1 represents the average speed of Laura in miles per hour. S (t) in Equation 1 also represent the speed of Laura in miles per hour. So, we can replace x by S (t) in Equation 2 and generate an equation of Distance in terms of temperature "t" as shown below:

D (S (t)) = 0.5 (6 + 0.1 (80-t))

D (t) = 3 + 0.0 (80 - t)

This expression models the distance that Laura runs in 30 minutes given that it is t∘F outside at the start of her run.