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.