Question

at a factory workers are draining a large vat containing water. the water is being drained at a constant rate. the table below shows the amount of water in the vat after different amounts of time.

time (minutes)	15	20	25	30

answer the following questions.
(a) how much water was in the vat when the workers started draining it?
$square$ liters
(b) choose the statement that best describes how the time and the amount of water in the vat are related. then give the value requested.
$circ$ as time increases, the amount of water in the vat decreases.
at what rate is the amount of water in the vat decreasing?
$square$ liters per minute
$circ$ as time increases, the amount of water in the vat increases.
at what rate is the amount of water in the vat increasing?
$square$ liters per minute

Explanation:

Step1: Find drainage rate

Calculate change in water over time:
$\text{Rate} = \frac{590 - 500}{15 - 20} = \frac{90}{-5} = -18$ liters per minute

Step2: Calculate initial water volume

Use linear formula $V(t) = V_0 + rt$. Substitute $t=15$, $V=590$, $r=-18$:
$590 = V_0 + (-18)(15)$
$590 = V_0 - 270$
$V_0 = 590 + 270 = 860$

Step3: Select correct relationship

Time increases, water decreases, rate is -18 (18 liters per minute draining).

Answer:

(a) 860 liters
(b)

• Selected statement: As time increases, the amount of water in the vat decreases.
• Rate of decrease: 18 liters per minute
• Rate of increase: 0 liters per minute