The time t required to drive a certain distance varies inversely with the speed, r. If it takes 2 hours to drive the distance at 67 miles per hour, how long will it take to drive the same distance at 55 miles per hour?
A. about 1.64 hours
B. about 134.00 hours
C. about 2.45 hours
D. about 61.00 hours
We can use the formula for inverse variation:
t = k/r
where k is a constant. We can solve for k by plugging in the given values for t and r:
2 = k/67
k = 134
Now we can use this value of k to find the time required at 55 miles per hour:
t = 134/55
t ≈ 2.45 hours
Therefore, the answer is choice C, about 2.45 hours.
Let's use the formula for inverse variation:
t = k/r
where t is the time, r is the speed, and k is a constant.
To find the constant, we can use the given information that it takes 2 hours to drive the distance at 67 miles per hour:
2 = k/67
To solve for k, we can cross multiply:
k = 2 * 67
k = 134
Now we have the constant k.
To find the time it will take to drive the same distance at 55 miles per hour, we can use the formula:
t = k/r
Substituting the values:
t = 134/55
Simplifying:
t ≈ 2.436363636...
So, it will take about 2.44 hours to drive the same distance at 55 miles per hour. Rounded to the nearest hundredth, the answer is approximately 2.44 hours.
Therefore, the correct answer is C. about 2.45 hours.