Question

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)

Answer 1

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:

`(t)/(7)-(t)/(10)=1`

Solving the above equation-

`\begin{gathered} 10t-7t=70 \\ 3t=70 \\ t=(70)/(3)\text{ hrs} \\ t=23(1)/(3)\text{ hrs or }23.33\text{ hrs} \end{gathered}`

Final Answer: It will take 23.33 hours.