Question

At 8:00 A.M., Brittany started filling a 3,200-gallon pond. At 10:00 A.M., she had filled 1,600 gallons. At what time will the pond be full?

Answer 1

To determine when the pond will be full, we first calculate the rate at which Brittany is filling the pond.

From 8:00 A.M. to 10:00 A.M., she filled 1,600 gallons over a period of 2 hours. Therefore, her filling rate is:

\[
\text{Rate} = \frac{\text{Gallons filled}}{\text{Time}} = \frac{1600 \text{ gallons}}{2 \text{ hours}} = 800 \text{ gallons per hour}
\]

Next, we need to know how much more water is needed to fill the pond. Since the pond has a total capacity of 3,200 gallons and she has already filled 1,600 gallons, the remaining amount to be filled is:

\[
\text{Remaining gallons} = 3200 \text{ gallons} - 1600 \text{ gallons} = 1600 \text{ gallons}
\]

Now we calculate how long it will take to fill the remaining 1,600 gallons at her rate of 800 gallons per hour:

\[
\text{Time needed} = \frac{\text{Remaining gallons}}{\text{Rate}} = \frac{1600 \text{ gallons}}{800 \text{ gallons per hour}} = 2 \text{ hours}
\]

Now, we add this time to 10:00 A.M. to find out when the pond will be full:

\[
10:00 \text{ A.M.} + 2 \text{ hours} = 12:00 \text{ P.M.}
\]

Thus, the pond will be full at:

\[
\boxed{12:00 \text{ P.M.}}
\]