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?
(1 point)
• about 1.64 hours
• about 134.00 hours
• about 2.45 hours
• about 61.00 hours
To solve this problem, we can set up the equation for inverse variation:
t = k/r
where t is the time, r is the speed, and k is the constant of proportionality.
Given that it takes 2 hours to drive the distance at 67 miles per hour, we can plug in these values to find k:
2 = k/67
k = 134
Now we can use this value of k to find the time it will take to drive the same distance at 55 miles per hour:
t = 134/55
t ≈ 2.45 hours
Therefore, it will take about 2.45 hours to drive the same distance at 55 miles per hour. The correct answer choice is:
• about 2.45 hours