A tank can be filled by Pipe A in 4 hours and by Pipe B in 6 hours. If both pipes are opened together, but Pipe B is closed after 2 hours, how long will it take to fill the tank?
["Title: How Long Does It Take to Fill the Tank When Pipe A Runs Alone for 2 Hours, Then Pipe B Joins and Is Closed?", "When dealing with tank-filling scenarios involving multiple pipes, understanding rates of flow and timing is crucial. A common practical example is two pipes filling a tank: Pipe A fills it in 4 hours, while Pipe B fills it in 6 hours. But what happens when Pipe B starts late and is closed after just 2 hours? This article breaks down the mathematics and explains step-by-step how long it truly takes to fill the tank under these conditions.", "---", "### Understanding the Flow Rates", "First, we calculate the individual filling rates:", "- Pipe A fills the tank in 4 hours → its rate is\n [\n \frac{1 \ ext{ tank}}{4 \ ext{ hours}} = 0.25 \ ext{ tanks/hour}\n ]", "- Pipe B fills the tank in 6 hours → its rate is\n [\n \frac{1 \ ext{ tank}}{6 \ ext{ hours}} \approx 0.1667 \ ext{ tanks/hour}\n ]", "---", "### Step-by-step Timeline of the Process", "Duration 1: Both Pipe A and Pipe B Open for 2 Hours", "During the first 2 hours, both pipes operate together. Their combined rate is:\n[\n0.25 + 0.1667 = 0.4167 \ ext{ tanks/hour}\n]", "Amount filled in 2 hours:\n[\n0.4167 \ imes 2 = 0.8333 \ ext{ (or } \frac{5}{6} \ ext{ of the tank)}\n]", "---", "### Remaining Tank to Fill After 2 Hours", "Total tank capacity is 1 unit, so remaining volume:\n[\n1 - \frac{5}{6} = \frac{1}{6} \ ext{ of the tank}\n]", "---", "### Step 2: Only Pipe A Continues After Pipe B Closes", "After 2 hours, Pipe B closes, and only Pipe A continues. Since Pipe A fills at 0.25 tanks/hour, the time ( t ) required to fill the remaining ( \frac{1}{6} ) tank is:\n[\nt = \frac{\ ext{Remaining volume}}{\ ext{Rate of Pipe A}} = \frac{\frac{1}{6}}{0.25} = \frac{1}{6} \div \frac{1}{4} = \frac{1}{6} \ imes 4 = \frac{4}{6} = \frac{2}{3} \ ext{ hours}\n]", "---", "### Total Time to Fill the Tank", "Add both durations:\n- First 2 hours (both pipes open)\n- Then ( \frac{2}{3} ) hours (only Pipe A)", "Total time:\n[\n2 + \frac{2}{3} = \frac{6}{3} + \frac{2}{3} = \frac{8}{3} \ ext{ hours}\n]", "That is approximately 2 hours and 40 minutes.", "---", "### Final Answer", "It takes (\frac{8}{3}) hours, or about 2 hours and 40 minutes, to fill the tank if Pipe A runs alone for 2 hours, then Pipe B closes and Pipe A continues until full.", "---", "### Why This Matters", "Understanding how partial operations and staggered inputs affect tank filling is valuable in plumbing, irrigation systems, and industrial process control. By calculating time precisely, waste can be minimized, and efficiency maximized.", "---", "Keywords: tank filling time, pipe A fills in 4 hours, pipe B fills in 6 hours, combined pipe operation, delayed pipe closure, flow rate calculation, how long to fill tank, tank filling timing problem.", "---", "If you’re managing a system with two pipes working together but with one starting late, this formula helps plan operations accurately — ensuring timely and efficient tank filling every time."]
