Question

Hudson is already 40 miles away from home on his drive back to college. He is driving 65 mi/h. Write an equation that models the total distance (D) traveled after (H) hours.

Answer 1

The equation modeling the total distance Hudson has traveled after H hours, given his initial distance of 40 miles from home and his speed of 65 mi/h, is D = 40 + 65H.

Step-by-step explanation:

To model the total distance (D) traveled by Hudson after (H) hours, we need to take into account the initial distance he is from home and the speed at which he is traveling. The equation that represents this scenario is:

D = 40 + 65H

Here, the 40 miles is the distance Hudson is already away from home. The 65 mi/h is his constant speed. For every hour (H) that Hudson drives, he covers an additional 65 miles. Therefore, after H hours, he will have traveled 65H miles. Adding the initial 40 miles to this, we get the total distance (D) he has covered from home.

This equation is a linear relationship, where the slope represents the speed, the y-intercept represents the starting point, and 'H' is the independent variable representing time in hours.