whirlpool 8.7 10

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
3
inches can fill the tub in
7
?minutes, how long will it take the tub to fill if a pipe of radius
4.5
inches is? used?


The tub would fill in approximately
_____ minutes.

Answer 1

t = time to fill tub

 

r = radius of pipe

 

t proportional to 1/r² means that

 

t = A/r²

 

where A is a constant.

 

Find A from knowing that with a 3 inch radius pipe, the tub is filled in 7 minutes.

 

7 min = A / (3 in)² ⇒ A = 63 min*in²

 

Then

 

t = 63/r² 

 

with r in inches, t in minutes.

 

For r = 4.5 inches,

 

t = 63 / (4.5)² min = 3.11 minutes