SOLUTION: Water pours into a container at a constant rate of 4 litres per minute. When there are 50 litres of water in the container, a pump begins to pump water out at a rate of 5 litres pe

Question 297131: Water pours into a container at a constant rate of 4 litres per minute. When there are 50 litres of water in the container, a pump begins to pump water out at a rate of 5 litres per minute. How many minutes will it take to empty the container?
(A) 10 (B) 24 (C) 50 (D) 120 (E) None of these
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
Rate * Time = Units

Rate of water pouring into the container is 4 liters per minute.

Rate of water being pumped out of the container is 5 liters per minute.

The net rate of water leaving the container is equivalent to 1 liter per minute.

When there are 50 liters of water in the container, the equation becomes:

1 * Time = 50

Time = 50 minutes.

It would take 50 minutes to empty the container assuming that water is pouring in at 4 liters per minute and water is being pumped out at 5 liters per minute.

Look at it from the perspective of the actual rates and you'll see how this works.

There are 50 liters of water in the tank.

Water is pouring in at 4 liters per minute for the next 50 minutes.

50 * 4 = 200 liters on top of the 50 liters that are already in the tank making a total of 250 liters.

In the same 50 minutes, the pump is taking water out of the container at 5 liters per minute.

50 * 5 = 250 liters of water being pumped out of the container.

This leaves the container empty after 50 minutes since the same amount of water that was pouring in, plus the amount of water that was already in the containter, has been pumped out.

The equation that we used was 1 * T = 50 which made T = 50.

T represents Time.

We could have used another equation as follows:

4*T + 50 = 5*T

When the values are equal, the tank is empty because 4*T + 50 is the number of liters of water coming in (we start at 50), and 5*T is the number of liters of water going out.

Solve for this equation to get:

T = 50.

Same answer.

In 50 minutes, the tank will be empty.

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