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6. It takes one hour longer to fill the empty pool when only the input pipe is open than it takes to empty the filled pool when only the drain pipe is open. It takes 72 hours to empty the filled pool when both pipes are open. How many hours does it take to fill the empty pool when only the input pipe is open

Respuesta :

Using the together rate, it is found that it takes 144.5 hours to fill the empty pool when only the input pipe is open.

What is the together rate?

It is the sum of each separate rate.

In this problem:

  • The input's pipe rate is 1/x.
  • The drain's pipe rate is of 1/(x-1).
  • The together rate is of 1/72.

Hence:

[tex]\frac{1}{x} + \frac{1}{x - 1} = \frac{1}{72}[/tex]

[tex]\frac{x - 1 + x}{x(x - 1)} = \frac{1}{72}[/tex]

[tex]x^2 - x = 144x - 72[/tex]

[tex]x^2 - 145x + 72 = 0[/tex]

Which is a quadratic equation with coefficients a = 1, b = -145, c = 72, hence:

[tex]\Delta = b^2 - 4ac = (-145)^2 - 4(1)(72) = 20737[/tex]

[tex]x_1 = \frac{145 + \sqrt{20737}}{2} = 144.5[/tex]

[tex]x_2 = \frac{145 - \sqrt{20737}}{2} = -0.5[/tex]

Time is a positive measure, hence, it takes 144.5 hours to fill the empty pool when only the input pipe is open.

More can be learned about the together rate at https://brainly.com/question/25159431

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