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 30water (liters) 610 540 470 400answer the following questions.(a) how much water was in the vat when the workers started draining it?__ 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.○ 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

Explanation:

Step1: Find rate of water change

Calculate change in water over time:
$\frac{540 - 610}{20 - 15} = \frac{-70}{5} = -14$ liters per minute

Step2: Calculate initial water amount

Use time=15, water=610, reverse the rate:
Initial amount $= 610 + (14 \times 15) = 610 + 210 = 820$ liters

Step3: Confirm relationship and rate

As time increases, water decreases. The magnitude of the rate is 14 liters per minute.

Answer:

(a) 820
(b) As time increases, the amount of water in the vat decreases.
14