Ein Wassertank kann von zwei Rohren, A und B, in 4 Stunden bzw. 6 Stunden gefüllt werden. Wenn beide Rohre gleichzeitig geöffnet werden, wie lange dauert es, den Tank zu füllen?

["How Long Does It Take to Fill a Water Tank When Two Pipes Work Together? A Practical Tutorial for Common Plumbing Problems", "When managing water tanks and plumbing systems, a common question arises: If two pipes can fill a tank in different times—Pipe A in 4 hours and Pipe B in 6 hours—how long will it take to fill the tank if both are opened simultaneously? This classic rate-based problem highlights efficient teamwork, even in plumbing.", "### Understanding the Fill Rates", "First, let’s determine the filling rate of each pipe:", "- Pipe A fills the tank in 4 hours → In 1 hour, it fills ( \frac{1}{4} ) of the tank.\n- Pipe B fills the tank in 6 hours → In 1 hour, it fills ( \frac{1}{6} ) of the tank.", "### Combined Fill Rate", "When both pipes are opened at the same time, their rates combine:", "[\n\ ext{Combined rate} = \frac{1}{4} + \frac{1}{6}\n]", "To add these fractions, find a common denominator:", "[\n\frac{1}{4} = \frac{3}{12}, \quad \frac{1}{6} = \frac{2}{12}\n]", "[\n\frac{3}{12} + \frac{2}{12} = \frac{5}{12}\n]", "So, together, the pipes fill ( \frac{5}{12} ) of the tank per hour.", "### Time to Fill the Tank", "To find how long it takes to fill the entire tank, take the reciprocal of the combined rate:", "[\n\ ext{Time} = \frac{1}{\frac{5}{12}} = \frac{12}{5} = 2.4 \ ext{ hours}\n]", "Converting 0.4 hours to minutes:\n( 0.4 \ imes 60 = 24 ) minutes.", "### Final Answer", "It takes 2 hours and 24 minutes to fill the tank when both Pipe A and Pipe B are opened simultaneously.", "---", "### Real-World Application", "This math applies to many household and industrial water systems—sewer drainage, irrigation tanks, or home plumbing within a building. Understanding how combined rates affect flow efficiency helps with scheduling, resource planning, and troubleshooting filling times.", "For any tank-filling scenario with multiple inlets, simply divide total work (1 full tank) by the combined rate—the same logical approach used here.", "---", "Keywords: water tank filling, plumbing rates, Pipe A 4 hours, Pipe B 6 hours, combined fill time, plumbing math, how long to fill a tank, tank filling rate problem."]