The number of minutes needed to drain a bathtub, m, varies inversely as the rate of draining, r. At 20 liters per minute, a bathtub can drain in 8 minutes. How many minutes would it take to drain the bathtub if the rate of drainage was 32 liters per minute?

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.