the amount of time

Question

The amount of time it takes to fill a whirlpool tub is inversely proportional to the square of the radius of the pipe used to fill it. If a pipe of radius
2.5
inches can fill the tub in
5
?minutes, how long will it take the tub to fill if a pipe of radius
4
inches is? used?

Answer 1

Let t = time (minutes), r = radius (inches)

 

The time is inversely proportional to the square of the radius:

 

t = k/r² (k is the proportionality constant) *this will be the equation that you will use all throughout*

 

For the first condition, they gave r = 2.5 and t = 5, so that you can solve for k:

 

5 = k/2.5² 

 

k = 31.25

 

In the second condition, they gave r = 4 and is asking for t. But this time you already have a value for k:

 

t = 31.25/4² 

 

t = 1.95 mins

Answer 2

Jessica, this is similar to the other problem, except both things are headed in opposite directions. It makes sense that the time for a larger pipe to fill the tub is going to be less.

 

This time y = k/x, so k = xy

 

From our problem, k = 2.5(5) = 12.5

 

y = 12.5/4 = 3.125 minutes.