A tank at a factory contains water. Workers are draining the tank at a constant rate. After 32 minutes of being drained, the tank contains 484 liters of water. After 54 minutes, the tank contains 198 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
A. As time increases, the amount of water in the tank decreases.
or
B. As time increases, the amount of water in the tank increases.
(b)How much water did the tank contain when the workers started draining it?
(a) The statement that best describes how the time and the amount of water in the tank are related is A. As time increases, the amount of water in the tank decreases.
(b) When the workers started draining the tank, it contained 484 liters of water.
Thank you. But for part a) what is the liters per min?
To determine the liters per minute at which the tank is being drained, we can calculate the rate of change in the amount of water in the tank.
We are given two data points:
- After 32 minutes, the tank contains 484 liters of water.
- After 54 minutes, the tank contains 198 liters of water.
To find the rate of change, we can subtract the initial amount from the final amount and divide by the time difference:
Rate of change = (final amount - initial amount) / time difference
Rate of change = (198 liters - 484 liters) / (54 minutes - 32 minutes)
Rate of change = (-286 liters) / (22 minutes)
Rate of change ≈ -13 liters/minute
Therefore, the tank is being drained at a rate of approximately 13 liters per minute.
(a) The statement that best describes how the time and the amount of water in the tank are related is:
B. As time increases, the amount of water in the tank decreases.
To determine the relationship between time and the amount of water in the tank, we can observe that as the tank is being drained at a constant rate, the amount of water decreases over time.
(b) To find out how much water the tank contained when the workers started draining it, we can use a linear equation.
Let's assume the amount of water in the tank when the workers started draining it is represented by "W0" (in liters) and the constant rate at which the water is being drained is represented by "d" (in liters per minute).
Given that after 32 minutes, the tank contains 484 liters of water, we can write the equation:
W0 - 32d = 484
Also, given that after 54 minutes, the tank contains 198 liters of water, we can write another equation:
W0 - 54d = 198
To solve these two equations simultaneously, we can subtract the second equation from the first:
(W0 - 32d) - (W0 - 54d) = 484 - 198
W0 - 32d - W0 + 54d = 286
22d = 286
d = 286/22
d ≈ 13.00
Substituting the value of d into either of the initial equations, we can find W0:
W0 - 32(13) = 484
W0 - 416 = 484
W0 = 484 + 416
W0 = 900
Therefore, when the workers started draining the tank, it contained 900 liters of water.