A tank can be filled by one pipe in 4 hours and drained by another pipe in 6 hours. If both pipes are opened simultaneously, how long will it take to fill the tank?
["Title: How Long Does It Take to Fill a Tank When One Pipe Fills It in 4 Hours and Another Drains It in 6 Hours?", "---", "When faced with a common fluid dynamics scenario involving filling and draining, many wonder: If a tank fills through one pipe in 4 hours and drains through another in 6 hours, how long will it take to fill the tank when both pipes are open simultaneously? This question explores the real-world application of rates and combined work, making it a great example for homeowners, engineers, and students alike. Let’s break down the solution step-by-step.", "---", "### Understanding the Filling and Draining Rates", "First, let’s convert the filling and draining into measurable rates:", "1. Filling Rate:\n A pipe fills the tank in 4 hours ⇒ Filling rate = 1 tank / 4 hours = 0.25 tanks per hour", "2. Draining Rate:\n A second pipe empties the tank in 6 hours ⇒ Draining rate = 1 tank / 6 hours ≈ 0.1667 tanks per hour", "When both pipes operate at the same time, their rates combine:", "- Net filling rate = Filling rate – Draining rate\n [\n \ ext{Net rate} = 0.25 - 0.1667 = 0.0833 \ ext{ tanks per hour}\n ]", "This equivalent of 1/12 tanks per hour means the tank fills at a rate of one-twelfth per hour.", "---", "### Calculating the Time to Fill the Tank", "To determine how long it takes to fill one full tank at the net rate of 0.0833 tanks per hour:", "[\n\ ext{Time} = \frac{1 \ ext{ tank}}{0.0833 \ ext{ tanks/hour}} \approx 12 \ ext{ hours}\n]", "For a precise calculation instead of decimal approximations:", "[\n\ ext{Net rate} = \frac{1}{4} - \frac{1}{6} = \frac{3 - 2}{12} = \frac{1}{12} \ ext{ tanks/hour}\n]", "Thus,\n[\n\ ext{Time} = \frac{1}{1/12} = 12 \ ext{ hours}\n]", "---", "### Summary", "- Filling rate: 1 tank in 4 hours → 0.25 tanks/hour\n- Draining rate: 1 tank in 6 hours → 0.1667 tanks/hour\n- Net rate: 0.25 – 0.1667 = 0.0833 tanks/hour\n- Time to fill tank: 12 hours", "---", "### Real-World Applications", "This type of problem explains how multiple inputs affect system capacity—useful in plumbing, hydraulic engineering, irrigation, and even everyday tasks like filling a swimming pool with both inlet and outlet controls.", "---", "### Final Takeaway", "When one pipe fills a tank in 4 hours and another drains it in 6 hours, both pipes open together will fill the tank in exactly 12 hours. Recognizing net rates empowers efficient resource management in fluid systems.", "---", "Keywords: fill tank pipe rate, draining pipe calculation, how long to fill tank with filling and draining pipes, net filling rate, real-world pipe filling problem", "---", "Want more practical physics and engineering calculations? Subscribe for weekly tips!"]
