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?

about 3.11 hours
140 hours
about 5.14 hours
393.75 hours

I think A

Yes.

To solve this problem, we can use the inverse variation formula, which states that the time (t) and speed (r) are inversely proportional. Mathematically, this can be represented as t = k/r, where k is the constant of variation.

Given that it takes 4 hours to drive the distance at 35 miles per hour, we can use this information to find the value of k.

Substituting the values into the formula:

4 = k/35

To solve for k, we can multiply both sides of the equation by 35:

4 * 35 = k

The product of 4 and 35 is 140, so k = 140.

Now that we have the value of k, we can use it to find the time required to drive the same distance at 45 miles per hour. Substituting the values into the formula:

t = 140/45

Dividing 140 by 45 gives us the result:

t ≈ 3.11 hours

Therefore, it will take about 3.11 hours to drive the same distance at 45 miles per hour.