Calculate Individual Rates:

1. Pipe A fills the tank in 10 hours:  $\frac{1}{10}\backslash frac\{1\}\{10\}$​ of the tank per hour.
2. Pipe B fills the tank in 15 hours:  $\frac{1}{15}\backslash frac\{1\}\{15\}$​ of the tank per hour.
3. Pipe C empties the tank in 20 hours:  $\frac{1}{20}\backslash frac\{1\}\{20\}$ of the tank per hour.

Find the Combined Rate:

• Combined filling rate of A and B:   $\frac{1}{10}+\frac{1}{15}=\frac{5}{30}=\frac{1}{6}\backslash frac\{1\}\{10\}\; +\; \backslash frac\{1\}\{15\}\; =\; \backslash frac\{5\}\{30\}\; =\; \backslash frac\{1\}\{6\}$ ​
• Subtract the emptying rate of C:    $\frac{1}{6}-\frac{1}{20}=\frac{7}{60}\backslash frac\{1\}\{6\}\; –\; \backslash frac\{1\}\{20\}\; =\; \backslash frac\{7\}\{60\}$ ​

Calculate the Time to Fill the Tank:

• The combined rate is $\frac{7}{60}\backslash frac\{7\}\{60\}$​ of the tank per hour.
• Time to fill the tank: $\frac{60}{7}\backslash frac\{60\}\{7\}$​ hours, which is approximately 8 hours and 34 minutes

Answer: It will take approximately 8 hours and 34 minutes to fill the tank.