Question

The distance away from the city of Bloomsfield is a function of time. The function D(h)=440-65h represents the distance in miles away from Bloomsfield as you travel toward the city, based on the number of hours, h, you traveled. Find the distance left to get to Bloomsfield after 3 1/2 hours of traveling.

Answer 1

To find the distance left to get to Bloomsfield after 3 1/2 hours of traveling, we need to evaluate the function $D(h)$ at $h=3.5$.

The function given is:

$$D(h)=440-65h$$

Now we substitute $h=3.5$:

$$D(3.5)=440-65(3.5)$$

Calculating $65(3.5)$:

$$65\times 3.5=227.5$$

Now we can substitute this value back into the equation:

$$D(3.5)=440-227.5$$

Finally, we perform the subtraction:

$$D(3.5)=440-227.5=212.5$$

Therefore, the distance left to get to Bloomsfield after 3 1/2 hours of traveling is $\boxed{{\displaystyle 212.5}}$ miles.