The distance away from the city of Bloomsfield is a function of time. The function D(h)=440−65h

Question

represents the distance in miles away from Bloomsfield as you travel toward the city, based on the number of hours, h , you have traveled. Find the distance left to get to Bloomsfield after 3/12
hours of traveling. Enter your response in decimal form.(1 point)
The distance that you have left to travel i

Answer 1

To find the distance left to reach Bloomsfield after \( \frac{3}{12} \) hours of traveling, we first simplify the fraction \( \frac{3}{12} \) to \( \frac{1}{4} \) hours.

Next, we can substitute \( h = \frac{1}{4} \) into the function \( D(h) = 440 - 65h \):

\[ D\left(\frac{1}{4}\right) = 440 - 65\left(\frac{1}{4}\right) \]

Now, calculate \( 65 \times \frac{1}{4} \):

\[ 65 \times \frac{1}{4} = \frac{65}{4} = 16.25 \]

Now substitute that back into the distance function:

\[ D\left(\frac{1}{4}\right) = 440 - 16.25 = 423.75 \]

Thus, the distance left to get to Bloomsfield after \( \frac{3}{12} \) hours of traveling is \( \boxed{423.75} \) miles.