21. 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?
We can start by using the inverse variation formula:
t = k/r
where k is the constant of variation. To find k, we can use the given information that it takes 12 hours to drive the distance at 60 miles per hour:
12 = k/60
Multiplying both sides by 60, we get:
k = 720
Now we can use this value of k to find the time required to drive the same distance at 85 miles per hour:
t = 720/85
t ≈ 8.47 hours
Therefore, it will take approximately 8.47 hours to drive the same distance at 85 miles per hour.
To solve this problem, we can use the inverse variation equation, which states that when two variables, t and r, are inversely proportional, their product is constant. The equation can be written as:
t * r = k
where k is the constant of variation.
Given that it takes 12 hours to drive the distance at 60 miles per hour, we can substitute these values into the equation:
12 * 60 = k
Simplifying, we find that k = 720.
Now, we can use this value to determine how long it will take to drive the same distance at 85 miles per hour. Let's call this time "t2".
t2 * 85 = 720
Dividing both sides of the equation by 85:
t2 = 720 / 85
Evaluating the right side of the equation, we find:
t2 ≈ 8.47
Therefore, it will take approximately 8.47 hours (or approximately 8 hours and 28 minutes) to drive the same distance at 85 miles per hour.