Question

Laura is driving to Seattle. Suppose that the remaining distance to drive (in miles) is a linear function of her driving time (in minutes). When graphed, the function gives a line with a slope of -0.75 . See the figure below.Laura has 51 miles remaining after 33 minutes of driving. How many miles were remaining after 15 minutes of driving?

Answer 1

Laura has 64.5 miles remaining after 15 minutes of driving.

Explanation:

Laura is driving to Seattle. Suppose that the remaining distance to drive (in miles) is a linear function of her driving time (in minutes).

Slope of the function = -0.75

Laura has 51 miles remaining after 33 minutes of driving. It means the the line passes through the point (33,51).

The point slope form of a line is

`y-y_1=m(x-x_1)`

The equation of line is

`y-51=-0.75(x-33)`

`y-51=-0.75x+24.75`

Add 51 on both sides.

`y=-0.75x+24.75+51`

`y=-0.75x+75.75`

We need to find how many miles were remaining after 15 minutes of driving.

Substitute x=15 in the above equation.

`y=-0.75(15)+75.75`

`y=64.5`

Therefore, Laura has 64.5 miles remaining after 15 minutes of driving.