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
water (liters) 590 500 410 320
answer the following questions.
(a) choose the statement that best describes how the time and the amount of water in the vat are related. then give the value requested.
as time increases, the amount of water in the vat decreases.
at what rate is the amount of water in the vat decreasing?
liters per minute
as time increases, the amount of water in the vat increases.
at what rate is the amount of water in the vat increasing?
liters per minute
(b) how much water was in the vat when the workers started draining it?
liters

Explanation:

Step1: Analyze water-time relationship

Observe that as time increases, water amount drops: 590→500→410→320. So water decreases over time.

Step2: Calculate decrease rate

Take two time-water pairs: (15, 590) and (20, 500). Rate = $\frac{\text{Change in water}}{\text{Change in time}} = \frac{500 - 590}{20 - 15} = \frac{-90}{5} = -18$. The negative sign means 18 liters decrease per minute.

Step3: Find initial water amount

Use rate to find water at time 0. Water at 15 min: 590. Initial water = $590 + (15 \times 18) = 590 + 270 = 860$.

Answer:

(a)

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

(b) 860 liters