In the formula d = rt, the time t varies inversely with the rate r. A student running at 5 miles per hour runs one lap around the school campus in 8 minutes. If a second student takes 10 minutes to run one lap around the school, how fast is she running?

d = rt = 5 * 8/60 = ?

?/(10/60) = r = miles/hour

To determine the speed at which the second student is running, we can use the formula d = rt and the information given in the question.

First, let's convert the time values into hours since the rate is given in miles per hour. The first student takes 8 minutes to complete one lap, which is equivalent to 8/60 = 0.1333 hours.

Using the formula d = rt, we can substitute the values for the first student:
d = r * 0.1333
Since the distance is not given and both students are running one lap around the school campus, we can assume it is the same for both students and cancel out d.

Now let's calculate the speed for the second student. The second student takes 10 minutes to complete one lap, which is equivalent to 10/60 = 0.1667 hours.
So, we have the equation:
r * 0.1333 = r * 0.1667

To find the speed of the second student, we need to isolate r.

Dividing both sides of the equation by 0.1333, we get:
r = (r * 0.1667) / 0.1333

Simplifying, we have:
r = r * 1.250937734

Now, to isolate r, we divide both sides of the equation by r:
1 = 1.250937734

Since both sides of the equation are equal, this means that the value of r can be any real number.

Therefore, we cannot determine the exact speed at which the second student is running based on the given information.