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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.

Respuesta :

SaniShahbaz

Answer:

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.

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