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Officials begin to release water from a full man-made lake at a rate that would empty the lake in 6 weeks, but a river that can fill the lake in 20 weeks is replenishing the lake at the same time. How many weeks does it take to empty the lake? Express your answer as a fraction reduced to lowest terms, if needed.

Respuesta :

Answer:

[tex]8 \frac{4}{7}[/tex]

Step-by-step explanation:

The computation of the number of weeks taken for empty the lake is shown below:

Given that

Lake empty in 6 weeks

The River could fill the lake in 20 weeks

Let us assume the combined lake be x

So, here the equation is

[tex]\frac{1}{6} - \frac{1}{20} = \frac{1}{x}[/tex]

[tex]\frac{20 - 6}{6\times 20} = \frac{1}{x}[/tex]

[tex]\frac{14}{6\times 20} = \frac{1}{x}[/tex]

After solving this

x = [tex]\frac{60}{7} \\\\= 8 \frac{4}{7}[/tex]

hence the number of weeks that take for empty the lake is [tex]8 \frac{4}{7}[/tex]

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