A tank can be filled by two pipes. Pipe A fills it in 3 hours, and Pipe B fills it in 6 hours. How long will it take to fill the tank if both pipes are used together?
["How Long Does It Take to Fill a Tank When Two Pipes Work Together?", "When tackling household or industrial tasks like filling a tank, understanding how combined efforts can accelerate the process is invaluable. In this scenario, imagine a tank being filled by two pipes—Pipe A and Pipe B—each with distinct filling speeds: Pipe A fills the tank in 3 hours, while Pipe B fills it in 6 hours. But how long will it actually take if both pipes are used simultaneously?", "Let’s break down the problem using basic principles of work rates, a classic approach in time and work problems. The key idea is that each pipe contributes a portion of the tank filled per hour, and together they combine their work rates for a faster fill time.", "Step 1: Calculate Individual Work Rates", "- Pipe A fills the entire tank in 3 hours, so its work rate is:\n ( \frac{1 \ ext{ tank}}{3 \ ext{ hours}} = \frac{1}{3} ) of the tank per hour.", "- Pipe B fills the tank in 6 hours, so its work rate is:\n ( \frac{1 \ ext{ tank}}{6 \ ext{ hours}} = \frac{1}{6} ) of the tank per hour.", "Step 2: Combine the Rates", "When both pipes work together, add their hourly rates:\n[\n\frac{1}{3} + \frac{1}{6} = \frac{2}{6} + \frac{1}{6} = \frac{3}{6} = \frac{1}{2} \ ext{ tank per hour}\n]", "Step 3: Find the Total Time to Fill One Tank", "If both pipes together fill ( \frac{1}{2} ) of the tank each hour, then filling the full tank requires:\n[\n\ ext{Time} = \frac{1 \ ext{ tank}}{\frac{1}{2} \ ext{ tank/hour}} = 2 \ ext{ hours}\n]", "Conclusion", "Using both pipes simultaneously, the tank will be filled in just 2 hours—nearly double the speed compared to using just Pipe A alone, which would take 3 hours. This example highlights the power of teamwork: combining resources streamlines tasks and maximizes efficiency.", "If you're planning to fill a tank using multiple sources, whether in plumbing, construction, or industrial systems, understanding combined work rates helps optimize schedules, improve productivity, and better allocate resources. So the next time you’re working with cooperative pipes or systems, remember: working together often means moving faster!", "---", "Keywords: tank filling, Pipe A filling time, Pipe B filling time, combined work rates, math problem tank, time to fill tank, how long to fill tank with two pipes, equation pool filling, work rate formula tank."]
