Question

A public swimming pool that holds 45,000 gallons of water is going to be drained for maintenance at a rate of 100 gallons per minute. The amount of water, w
(in gallons), in the pool after t
minutes is given by the function w=45,000−100t
.

How many minutes will it take to empty the pool?

Answer 1

To find out how many minutes it will take to empty the pool, we need to determine when the amount of water \( w \) in the pool equals zero.

We start with the equation provided:

\[
w = 45,000 - 100t
\]

We set \( w \) to zero to find \( t \):

\[
0 = 45,000 - 100t
\]

Now, we can solve for \( t \):

\[
100t = 45,000
\]
\[
t = \frac{45,000}{100}
\]
\[
t = 450
\]

So, it will take 450 minutes to empty the pool.