The time,t, required to drive a certain distance varies inversely with speed,r. If it takes 12 hours to drive the distance at 60 miles per hour, how long will it take to drive the same disatcne at 85 miles per hour?

about 7.08 hours?
about 5.00?
or 8.47 hours?

please show me your work so i can undertstand!

t = k/s

12 = k/60
k = 12*60

t = (12*60) / 85
or
t = 8.47 hours

I'll take that as a no.

its different for everyone

do you have the rest of the answers for the test?

Well, let's start by writing down the given information. We know that the time, t, required to drive a certain distance varies inversely with the speed, r. In other words, we have the equation t = k/r, where k is a constant.

Now, we are given that it takes 12 hours to drive the distance at 60 miles per hour. So we can replace t with 12 and r with 60 in our equation to solve for k:

12 = k/60

To solve for k, we can cross multiply and get:

12 * 60 = k

k = 720

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 85 miles per hour. We can again use our equation:

t = k/r

t = 720/85

t ≈ 8.47

So, it will take about 8.47 hours to drive the same distance at 85 miles per hour.

Hope that helps! Drive safely and quickly, but not too quickly, or you might get a ticket!

To solve this problem, we use the concept of inverse variation. Inverse variation means that as one variable increases, the other variable decreases, and vice versa.

The equation that represents inverse variation is:

t = k/r

Where:
t = time taken to drive the distance
r = speed (miles per hour)
k = constant of variation

From the given information, we know that it takes 12 hours to drive the distance at a speed of 60 miles per hour. Using this information, we can substitute t = 12 and r = 60 into the equation to find the value of k.

12 = k/60

To solve for k, we multiply both sides of the equation by 60:

12 * 60 = k

k = 720

Now that we know the value of k, we can use it to find the time required to drive the same distance at a speed of 85 miles per hour. Let's substitute t = ? and r = 85 into the equation:

t = 720/85

Calculating the right side of the equation:

t ≈ 8.47

Therefore, it will take approximately 8.47 hours to drive the same distance at a speed of 85 miles per hour.

So, the correct answer is approximately 8.47 hours.