Question

A group of hikers park their car at a trail head and hike into the forest to a campsite. The next morning, they head out on a hike from their campsite walking at a steady rate. The graph shows their distance in miles, d, from the car on the day of their hike after h hours.

a. How far is the campsite from the car? How do you know?

b. Write an equation that describes the relationship between d and h.

c. After how many hours will the hikers be 24 miles from their car? How do you know?

Answer 1

a:3
h=1/3d+3
c: 7 hrs because they started at 3 miles away and went 3 mphs

Answer 2

a. 3

b. h = 1/3d + 3

c. 7 hours because they started at 3 miles and moved at a constant rate of 3 miles per hour

Explanation:

for question A it's 3 because they went on a hike from their campsite, not their car and the graph is the distance from their car since the graph starts at 3 this means that the campsite is 3 miles from their car.

for question B it's h = 1/3d because if you look at the graph you can take where two of the points on the line are on a cross-section of the graph and see how many hours and miles there are between the two, then just take the y-intercept or in this case the h intercept and put it after the x or in this case d. Then just simplify the equation, so that the y(d) side is equal to 1, ie: instead of 2y = 8x + 4 its y = 4x + 4.

and finally, for question C, you can just plug the x(d) and y(h) value that is given in this case d = 24, and plug it in so h = 1/3d + 3 becomes h = 24/3 + 3