Question

jane 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) 6 9 12 15
water (gallons) 118 142 166 190
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?
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?
gallons per minute
(b) how much water was already in the pool when jane started adding water?
gallons

Explanation:

Step1: Analyze water change over time

Check water change between 6-9 mins: $142 - 118 = 24$ gallons, time change: $9-6=3$ mins. Rate: $\frac{24}{3}=8$ gallons/min. Verify with 9-12 mins: $166-142=24$, $\frac{24}{3}=8$. So water increases over time.

Step2: Find initial water amount

Use linear relation $y=mx+b$, $m=8$. Plug $x=6, y=118$:
$118 = 8\times6 + b$
$118 = 48 + b$
$b = 118 - 48 = 70$

Answer:

(a) As time increases, the amount of water in the pool increases.
At what rate is the amount of water in the pool increasing?
8 gallons per minute
(b) 70 gallons