Question

david is adding water to a swimming pool at a constant rate. the table below shows the amount of water in the pool after different amounts of time.
time (minutes) | water (gallons)
8 | 163
12 | 207
16 | 251
20 | 295
answer the following questions.
(a) choose the statement that best describes how the time and the amount of water in the pool are related. then give the value requested.

• as time increases, the amount of water in the pool decreases. at what rate is the amount of water in the pool decreasing?

square gallons per minute

• as time increases, the amount of water in the pool increases. at what rate is the amount of water in the pool increasing?

square gallons per minute
(b) how much water was already in the pool when david started adding water?
square gallons

Explanation:

Step1: Analyze relationship trend

Compare time and water values: as time goes from 8→12→16→20 minutes, water goes from 163→207→251→295 gallons, so water increases with time.

Step2: Calculate the rate of increase

Use two data points to find the rate. Take (8, 163) and (12, 207):
$\text{Rate} = \frac{207 - 163}{12 - 8} = \frac{44}{4} = 11$ gallons per minute.

Step3: Find initial water amount

Use linear equation $y = mx + b$, where $y$ is water, $x$ is time, $m=11$. Substitute $x=8, y=163$:
$163 = 11\times8 + b$
$163 = 88 + b$
$b = 163 - 88 = 75$

Answer:

(a)

• Selected statement: As time increases, the amount of water in the pool increases.
• Rate: 11 gallons per minute

(b) 75 gallons