The time it takes you to get to campus varies inversely as your driving rate. Driving at a rate of 40 miles per hour, it takes 1.5 hours. How long would the trip take you driving at a rate of 60 miles per hour?

40*1.5 = 60

60t = 60, so the time would be 1 hour

or, since time*speed = a constant

(3/2 speed)(2/3 time) = the same constant
2/3 of 1.5 hours is 1 hour.

To find the time it would take you to drive at a rate of 60 miles per hour, we can use the concept of inverse variation.

Inverse variation means that as one variable increases, the other variable decreases, and vice versa. In this case, the driving rate is inversely related to the time it takes to get to campus.

We are given that driving at a rate of 40 miles per hour, it takes 1.5 hours. Let's call this time t1 and the driving rate r1.

t1 = 1.5 hours
r1 = 40 miles per hour

Now, if we want to find the time it would take when driving at a rate of 60 miles per hour (let's call it t2), we can set up the equation:

t1 * r1 = t2 * r2

Substituting the given values:

1.5 * 40 = t2 * 60

Now we can solve for t2:

60 = t2 * 60

Divide both sides of the equation by 60:

t2 = 60 / 60

Simplifying, we find:

t2 = 1 hour

Therefore, when driving at a rate of 60 miles per hour, the trip would take 1 hour.