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
We can start by using the formula for inverse variation: t = k/r, where k is a constant of proportionality. We can solve for k by plugging in the given values for t and r:
12 = k/60
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, the answer is (D) about 8.47 hours.
or, simply
x(85) = 12(60)
x = 720/85= 8.47 or appr 8.5 hours
Yes, that is another way to solve the problem using the property of inverse variation.
To find the time it takes to drive the same distance at 85 miles per hour, we can set up a proportion using the inverse relationship between time and speed.
Let t1 be the original time (12 hours) and r1 be the original speed (60 miles per hour). Let t2 be the time we want to find and r2 be the new speed (85 miles per hour).
The proportion can be written as:
t1 / r1 = t2 / r2
Plugging in the given values, we have:
12 / 60 = t2 / 85
To find t2, we can cross multiply and solve for it:
12 * 85 = 60 * t2
1020 = 60t2
t2 = 1020 / 60
t2 = 17
Therefore, it will take about 17 hours to drive the same distance at 85 miles per hour.
The answer is not one of the options provided.