Answer :
Answer
It will take 2 hours to fill the daily quota if all the machines are running.
Explanation
To find how long it takes to fill the daily quota if all the machines are running, we use the relation below:
Rate of machine 1 + Rate of machine 2 + Rate of machine 3 = Total rate of the machines
[tex]\begin{gathered} \Rightarrow\frac{1}{3}+\frac{1}{14}+\frac{1}{10.5}=\frac{1}{x} \\ \text{Where x is the }time\text{ it takes to fill the daily quota} \\ \frac{1}{3}+\frac{1}{14}+\frac{2}{21}=\frac{1}{x} \\ \text{Multiply all through by 42x} \\ 42x(\frac{1}{3})+42x(\frac{1}{14})+42x(\frac{2}{21})=42x(\frac{1}{x}) \\ 14x+3x+4x=42 \\ 21x=42 \\ x=\frac{42}{21} \\ x=2 \\ \text{Therefore it will take 2 hours to fill the daily quota} \end{gathered}[/tex]