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A winery has a vat with two pipes leading to it. The inlet pipe can fill the vat in 4 ​hours, while the outlet pipe can empty it in 10 hours. How long will it take to fill the vat if both pipes are left​ open?

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CorvoTheDishonored
10hours 10% per hour 

4hours 25% per hour

1hour mark it would have filled 15% it will fill 15% per hour period

100/15=6 2/3hours to fill it

The time it will take for the vat to get full if both pipes are open is;

t = ²⁰/₃ hours

We are told that;

Inlet pipe can fill the vat in 4 hours

Outlet pipe can empty in 10 hours

  • Let the time it will take for the vat to get full be t and thus from fractions, we can get;

1/4 - 1/10 = 1/t

I used negative in front of 1/10 because the outlet is taking water out of the tank

Thus;

1/4 - 1/10 = 1/t

Multiply through by 40 to get;

10 - 4 = 40/t

6 = 40/t

Cross multiply to get;

t = 40/6

t = ²⁰/₃ hours

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