Answer :
Answer:
5 minutes.
Step-by-step explanation:
We have been given that the number of minutes needed to drain a bathtub, m, varies inversely as the rate of draining, r.
We know that two inversely proportional quantities are in form [tex]y=\frac{k}{x}[/tex], where y is inversely proportional with x and k is constant of proportionality.
Upon substituting our given variables in inversely proportion, we will get:
[tex]m=\frac{k}{r}[/tex]
Let us find constant of proportionality using our given information.
[tex]8=\frac{k}{20}[/tex]
[tex]8\cdot 20=\frac{k}{20}\cdot 20[/tex]
[tex]k=160[/tex]
So our required equation would be [tex]m=\frac{160}{r}[/tex].
Now, we will substitute [tex]r=32[/tex] in our equation to solve for time.
[tex]m=\frac{160}{32}[/tex]
[tex]m=5[/tex]
Therefore, it will take 5 minutes to drain the bathtub at a rate of 32 liters per minute.