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.
20
25 30
500 410 320
Time (minutes) 15
Water (liters) 590
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.
O 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
O 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?
tr

Answer 1

There were 590 liters of water in the vat when the workers started draining it.

How to solve

From the table, we can see that the amount of water in the vat is decreasing as time increases. This means that the water in the vat is being drained at a constant rate.

To calculate the rate, we can find the slope of the line that connects the two points on the table.

rate = (320 - 590)/(30 - 15) = -17 liters/minute

The rate is negative because the amount of water is decreasing. Therefore, the amount of water in the vat is decreasing at a rate of 17 liters per minute.

(b) How much water was in the vat when the workers started draining it?

We can extrapolate the line back to time 0 to find the initial amount of water in the vat.

initial amount of water = 590 + (-17)(0) = 590 liters

Therefore, there were 590 liters of water in the vat when the workers started draining it.