Question

a tank at a factory contains water. workers are filling the tank at a constant rate. after 35 minutes of being filled, the tank contains 556 liters of water. after 55 minutes, the tank contains 836 liters of water.

(a) choose the statement that best describes how the time and the amount of water in the tank are related. then fill in the blank.

○ as time increases, the amount of water in the tank decreases.
the amount of water in the tank decreases at a rate of \\(\square\\) liters per minute.

○ as time increases, the amount of water in the tank increases.
the amount of water in the tank increases at a rate of \\(\square\\) liters per minute.

(b) how much water did the tank contain when the workers started filling it?
\\(\square\\) liters

Explanation:

Step1: Identify relationship & find rate

First, confirm that as time increases, the water amount rises (since 55 mins has more water than 35 mins). Calculate the rate:
$\text{Rate} = \frac{836 - 556}{55 - 35} = \frac{280}{20} = 14$ liters per minute.

Step2: Set up linear equation

Let $y$ = water in liters, $x$ = time in minutes. Use the linear form $y = mx + b$, where $m=14$. Substitute $x=35, y=556$:
$556 = 14 \times 35 + b$

Step3: Solve for initial water ($b$)

Calculate $14 \times 35 = 490$, then rearrange:
$b = 556 - 490 = 66$

Answer:

(a) As time increases, the amount of water in the tank increases.
The amount of water in the tank increases at a rate of 14 liters per minute.
(b) 66 liters