Using the together rate, it is found that the value that must be discarded is given by x = -9.
It is the sum of each separate rate.
In this problem, the rates are given as follows:
Hence:
[tex]\frac{1}{x} + \frac{1}{x + 18} = \frac{1}{40}[/tex]
[tex]\frac{x + 18 + x}{x(x + 18)} = \frac{1}{40}[/tex]
[tex]x^2 + 18x = 80x + 720[/tex]
[tex]x^2 - 72x - 720 = 0[/tex]
Then, we have a quadratic function, with coefficients a = 1, b = -72, c = -720, so:
[tex]\Delta = (-72)^2 - 4(1)(-720) = 8064[/tex]
[tex]x_1 = \frac{72 + \sqrt{8064}}{2} = 80.9[/tex]
[tex]x_2 = \frac{72 - \sqrt{8064}}{2} = -9[/tex]
They cannot have a negative rate, hence the value that must be discarded is given by x = -9.
More can be learned about the together rate at https://brainly.com/question/25159431
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