the time, t, required to drive a certain distance varies inversely with the speed, r .if it takes 8 hours to drive the distance at 45 miles per hour , how long will it take to drive the same distance at 65 miles per hour?

distance=rate times time

The distance should be 8 x 45 = 360

360 = 65 times ?

Thanks anonymous!❤️

To solve this problem, we can start by writing the inverse variation equation relating time and speed. The equation for inverse variation is:

t = k/r

Where t represents the time, r represents the speed, and k is the constant of variation.

We are given that it takes 8 hours (t = 8) to drive the distance at 45 miles per hour (r = 45). Let's use this information to find the value of k:

8 = k/45

To solve for k, we can multiply both sides of the equation by 45:

8 * 45 = k
k = 360

Now we can substitute the value of k into the inverse variation equation:

t = 360/r

We need to find the time it takes to drive the same distance at 65 miles per hour (r = 65). Let's plug in this value and solve for t:

t = 360/65

Calculating this, we get:

t ≈ 5.54

Therefore, it will take approximately 5.54 hours (or 5 hours and 33 minutes) to drive the same distance at 65 miles per hour.