# If both pipes are used together, how long will it take to fill 2/3 of the tank?

• MHB
In summary, the problem asks how long it will take to fill 2/3 of a tank using two inlet pipes, one of which fills the tank in 5 hours and the other in 3 hours. By setting up the equation (1/5) + (1/3) = 1/x and solving for x, we find that it would take 15/8 hours for the two pipes to fill one tank. Multiplying this by 2/3, we get 5/4 hours as the time it would take to fill 2/3 of the tank.

One inlet pipe fills an empty tank in 5 hours. A second inlet pipe fills the same tank in 3 hours. If both pipes are used together, how long will it take to fill 2/3 of the tank?

My Work:

Let x = time when both pipes are used together

(1/5) + (1/3) = 1/x

I found x to be 15/8 hours.

Must I now multiply (15/8)(2/3)?

RTCNTC said:
I found x to be 15/8 hours.

Must I now multiply (15/8)(2/3)?
Correct.
Yes.

Wilmer said:
Correct.
Yes.

It took several tries before I found the correct set up. Unfortunately, no such thing as ENOUGH TIME when taking a test.

That's why you "practice, practice, practice" before the test!

Country Boy said:
That's why you "practice, practice, practice" before the test!

My classroom days ended in December 1993.

Then what "test" were you talking about?

Test tickle?

As a slightly different way to approach this problem, we can see that working together for 15 hours, the two inlet pipes can fill 8 tanks, and so it would take 15/8 hours for the two pipes to fill one tank, and 2/3 of that time to fill 2/3 tank, since the two pipes flow presumably at constant rates. Hence:

$$\displaystyle t=\frac{2}{3}\cdot\frac{15}{8}\text{ hr}=\frac{5}{4}\text{ hr}$$

Wilmer said:
Correct.
Yes.

(15/8)(2/3) = 5/4 hrs

Stick a pink star on your forehead :)

## 1. How do you calculate the time it takes to fill 2/3 of the tank using both pipes?

In order to calculate the time it takes to fill 2/3 of the tank, you will need to know the flow rate of each pipe, the volume of the tank, and the amount of water already in the tank. Then, you can use the formula Time = Volume / (Flow rate of pipe 1 + Flow rate of pipe 2) to determine the time it takes.

## 2. What units should be used for the flow rate and volume in the calculation?

The flow rate should be measured in volume per unit time, such as gallons per minute or liters per hour. The volume of the tank should be measured in the same units as the flow rate, such as gallons or liters.

## 3. Can the time it takes to fill 2/3 of the tank vary depending on the flow rates of the pipes?

Yes, the time it takes to fill 2/3 of the tank can vary depending on the flow rates of the pipes. If one pipe has a higher flow rate, it will fill the tank faster and therefore reduce the overall filling time when used together with another pipe.

## 4. What happens if the tank is already partially filled when both pipes are turned on?

If the tank is already partially filled, the time it takes to fill 2/3 of the tank will be shorter because there is less volume to fill. The calculation will be the same, but the amount of water already in the tank should be subtracted from the total volume of the tank.

## 5. How accurate is the calculation for the time it takes to fill 2/3 of the tank using both pipes?

The accuracy of the calculation depends on the accuracy of the flow rate and volume measurements. If these values are accurately measured, then the calculation should provide a fairly accurate estimate of the time it takes to fill 2/3 of the tank using both pipes together.

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