The time t required to drive a certain distance varies inversely with the speed r. If it takes 4 hours to drive the distance at 35 miles per hour, how long will it take to drive the same distance at 45 miles per hour?
(1 point)
• about 3.11 hours
• 140 hours.
• about 5.14 hours
• 393.75 hours
To solve this problem, we can use the formula for inverse variation, which states that t = k/r, where t is the time, r is the speed, and k is the constant of variation.
Given that it takes 4 hours to drive the distance at 35 miles per hour, we can set up the following equation:
4 = k/35
To find the value of k, we can multiply both sides by 35:
k = 4 * 35
k = 140
Now that we have the value of k, we can use it to find the time it will take to drive the same distance at 45 miles per hour:
t = 140/45
t ≈ 3.11 hours
Therefore, it will take about 3.11 hours to drive the same distance at 45 miles per hour. The correct answer is:
about 3.11 hours