A tank can be filled by two pipes. Pipe A can fill it in 4 hours, and Pipe B can fill it in 6 hours. How long will it take to fill the tank if both pipes are used together?
["How Long Will It Take to Fill a Tank When Two Pipes Work Together?\nCombining Pipe A and Pipe B to Speed Up Filling", "When faced with the challenge of filling a tank quickly, a smart approach is to combine the strengths of multiple resources—exactly what happens when two pipes fill a tank simultaneously. In this article, we break down how long it takes to fill a tank when Pipe A and Pipe B are used together, given that Pipe A fills the tank in 4 hours and Pipe B in 6 hours.", "---", "## Understanding Individual Pipe Rates", "To determine how fast both pipes fill the tank together, start by calculating how much of the tank each pipe fills per hour:", "- Pipe A:\n Fills the tank in 4 hours → fills ( \frac{1}{4} ) of the tank per hour.", "- Pipe B:\n Fills the tank in 6 hours → fills ( \frac{1}{6} ) of the tank per hour.", "---", "## Calculating Combined Flow Rate", "When both pipes operate together, their filling rates add up:", "[\n\ ext{Combined rate} = \frac{1}{4} + \frac{1}{6}\n]", "To add these fractions, find the least common denominator (LCD), which is 12:", "[\n\frac{1}{4} = \frac{3}{12}, \quad \frac{1}{6} = \frac{2}{12}\n]", "[\n\ ext{Combined rate} = \frac{3}{12} + \frac{2}{12} = \frac{5}{12}\n]", "This means both pipes together fill ( \frac{5}{12} ) of the tank each hour.", "---", "## Finding the Total Time to Fill the Tank", "Let ( t ) be the time in hours required to fill the entire tank when working together. Using the rate:", "[\n\frac{5}{12} \ imes t = 1\n]", "Solve for ( t ):", "[\nt = \frac{1}{\frac{5}{12}} = \frac{12}{5} = 2.4 \ ext{ hours}\n]", "Convert 0.4 hours to minutes:\n[\n0.4 \ imes 60 = 24 \ ext{ minutes}\n]", "---", "## Final Result", "When Pipe A and Pipe B are used together, the tank will be completely filled in 2 hours and 24 minutes.", "---", "## Why This Approach Works", "Using multiple pipes to fill a tank demonstrates a practical application of work rate problems in math and real-life scenarios. Combining rates simplifies complex problems and helps optimize time—ideal knowledge for homeowners, contractors, and engineers alike.", "---\nKeywords: tank filling, pipe flow rate, work rate problem, Pipe A filling time, Pipe B filling time, combined work rate, how long to fill tank, math problem solution", "Meta Description:\nLearn how long it takes to fill a tank when two pipes work together—Pipe A fills in 4 hours, Pipe B in 6 hours. Find the combined filling time and step-by-step calculation."]
