The time, t, required to drive a certain distance varies inversely with the speed, r. If it takes 12 hours to drive the distance at 60 miles per hour, how long will it take to drive the same distance at 85 miles per hour?
A. About 7.08 hours
B. About 5.00 hours
C. About 1.42 hours
D. About 8.47 hours
t = k/r
12 = k/60
so
k = 12*60
then
t = 12*60/85 = 8.47
To solve this problem, we need to use the concept of inverse variation. Inverse variation states that if a variable y is inversely proportional to another variable x, then their product remains constant.
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.