A hot air balloon begins its descent at a rate of 22 1/2 feet per minute. How long will it take for the balloon's elevation to change by -315 feet?

315/22.5 = _______ minutes

To find out how long it will take for the balloon's elevation to change by -315 feet, we can use the equation:

Time = Change in Elevation / Rate of Descent

In this case, the change in elevation is -315 feet and the rate of descent is 22 1/2 feet per minute.

First, we need to convert the mixed number 22 1/2 into an improper fraction. To do this, we multiply the whole number (22) by the denominator (2) and add the numerator (1), then put the result over the denominator:

22 1/2 = (22 * 2 + 1) / 2 = 45/2

Now we can substitute these values into the equation:

Time = -315 / (45/2)

To divide by a fraction, we can multiply by its reciprocal:

Time = -315 * (2/45)

Next, we simplify:

Time = -630/45

To further simplify the fraction, we can divide the numerator and denominator by their greatest common divisor, which is 45:

Time = -14

Therefore, it will take approximately 14 minutes for the balloon's elevation to change by -315 feet.