t = k/r
12 = k/60
so
k = 12*60
then
t = 12*60/85 = 8.47
A. About 7.08 hours
B. About 5.00 hours
C. About 1.42 hours
D. About 8.47 hours
12 = k/60
so
k = 12*60
then
t = 12*60/85 = 8.47
In this case, the time required to drive a certain distance (t) varies inversely with the speed (r). Mathematically, we can express this relationship as t = k/r, where k is a constant.
We are given that it takes 12 hours to drive the distance at 60 miles per hour. Let's plug these values into the equation to find the constant k:
12 = k/60
To solve for k, we can multiply both sides of the equation by 60:
12 * 60 = k
k = 720
Now that we know the value of k, we can use it to find the time required to drive the same distance at 85 miles per hour:
t = k/r
t = 720/85
t ≈ 8.47 hours
Therefore, the answer is option D. It will take approximately 8.47 hours to drive the same distance at 85 miles per hour.