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A winery has a vat with two pipes leading to it. The inlet pipe can fill the vat in 7 hours, while the other outlet pipe can empty it in 10 hours. How long will it take to fill the vat if both pipes are left open?It will take ______ hours.(Simplify your answer. Do not round)

Sagot :

Given: A winery has a vat with two pipes leading to it. The inlet pipe can fill the vat in 7 hours, while the other outlet pipe can empty it in 10 hours.

Required: To determine how long it will take to fill the vat if both pipes are left open.

Explanation: Let t be the time to fill the vat when both valves are open.

Then filing the vat means plus while emptying means minus.

Let 1 denote the completely fill vat.

Then, according to the question:

[tex]\frac{t}{7}-\frac{t}{10}=1[/tex]

Solving the above equation-

[tex]\begin{gathered} 10t-7t=70 \\ 3t=70 \\ t=\frac{70}{3}\text{ hrs} \\ t=23\frac{1}{3}\text{ hrs or }23.33\text{ hrs} \end{gathered}[/tex]

Final Answer: It will take 23.33 hours.

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