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A large aquarium should contain 10,000 liters of water when it is filled correctly. It will overflow if it gets up to 12,000 liters. The fish will get sick if it gets down to 4,000 liters. The aquarium has an automatic system to help keep the correct water level. If the water level is too low, a faucet fills it. If the water level is too high, a drain opens. One day, the system stops working correctly. The faucet starts to fill the aquarium at a rate of 30 liters per minute, and the drain opens at the same time, draining the water at a rate of 20 liters per minute. How long will it take until the tank starts overflowing or the fish get sick (if it started with 10,000 liters of water)?

Respuesta :

Answer:

The water level is rising because it is filling 10 more liters than it is draining

16.7 hours

Step-by-step explanation:

The rate at which the tank is filled and the rate at which the tank is draining

are constant.

Correct response;

  • The tank will start overflowing after 3 hours and 20 minutes.

Method used to obtain the above response;

Given:

Volume of water in the aquarium = 10,000 liters

Volume level at which the tank overflows = 12,000 liters

Level of the volume at which the fish get sick = 4,000 liters

Rate at which water enters the tank = 30 liter per minute

Rate at which the tank is draining the water = 20 liters per minute

Required;

The time it will take until the tank starts overflowing.

Solution:

Water that needs to be added to the tank before it begins to overflow = 12,000 liters - 10,000 liters = 2,000 liters

Let x represent the time after which the tank starts overflowing, the

(constant) rate of change function that gives the time it takes for the water

to overflow is therefore;

30·x - 20·x = 2,000

10·x = 2,000

x = 200 minutes = 3 hours and 20 minutes

  • The time it to overflow is 3 hours 20 minutes.

Learn more about rate of change functions here:

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