Question

Rachel is driving to Las Vegas. 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 -0.95. See the figure below.
Rachel has 43 miles remaining after 49 minutes of driving. How many miles will be remaining after 57 minutes of driving?

Answer 1

Explanation:

To find the number of miles remaining after 57 minutes of driving, we can use the given information that the function has a slope of -0.95.

Let's denote the remaining distance in miles as "d" and the driving time in minutes as "t".

We are given two points on the line: (49, 43) and (57, ?). The first point indicates that after 49 minutes of driving, there are 43 miles remaining.

Using the point-slope form of a linear equation, we can calculate the equation of the line:

(y - y1) = m(x - x1),

where (x1, y1) is a point on the line and "m" is the slope.

Using (49, 43) as our point, the equation becomes:

(d - 43) = -0.95(t - 49).

Now, we can substitute t = 57 into the equation and solve for d:

(d - 43) = -0.95(57 - 49).

Simplifying:

(d - 43) = -0.95(8),

d - 43 = -7.6,

d = 43 - 7.6,

d ≈ 35.4.

Therefore, after 57 minutes of driving, approximately 35.4 miles will be remaining.