A research drone descends in stages into a vent at 3,600 meters. It goes down 1/4 of the depth, then 2/5 of the remaining, then 1/3 of what’s left. How many meters has it descended after all three stages?

["Title: How A Research Drone Descends Through a 3,600-Meter Vent: A Step-by-Step Breakdown of Its Descent", "Exploring the deep recesses of natural vents, especially at extreme altitudes like 3,600 meters, demands precision, endurance, and innovative engineering. One fascinating scenario involves a specialized research drone descending in carefully calculated stages—each fraction of its journey refining its position within a vent system. In this article, we analyze a precise descent pattern to determine the total meters descended through three progressive stages: first 1/4 of the depth, then 2/5 of what remains, and finally 1/3 of what’s left. Understanding this breakdown offers insight into the drone’s navigation and the engineering challenges of deep-vent exploration.", "### The Vent Descent: A Three-Stage Journey", "We begin with a vent depth of 3,600 meters. The drone descends in three distinct stages:", "Stage 1: The drone travels down 1/4 of the full depth.\nCalculate:\n[\n\ ext{Stage 1 descent} = \frac{1}{4} \ imes 3600 = 900 \ ext{ meters}\n]", "Remaining depth after Stage 1:\n[\n3600 - 900 = 2700 \ ext{ meters}\n]", "Stage 2: From the remaining depth of 2,700 meters, the drone descends 2/5 of it.\nCalculate:\n[\n\ ext{Stage 2 descent} = \frac{2}{5} \ imes 2700 = 1080 \ ext{ meters}\n]", "Remaining depth after Stage 2:\n[\n2700 - 1080 = 1620 \ ext{ meters}\n]", "Stage 3: Finally, the drone descends 1/3 of the remaining 1,620 meters.\nCalculate:\n[\n\ ext{Stage 3 descent} = \frac{1}{3} \ imes 1620 = 540 \ ext{ meters}\n]", "### Total Descent After All Three Stages", "To find the total descent, sum the distances traveled in each stage:\n[\n900 + 1080 + 540 = 2520 \ ext{ meters}\n]", "### Real-World Implications for Research and Engineering", "This precise tri-stage descent demonstrates the sophisticated control required in drone-based vent exploration. At 3,600 meters, environmental conditions—such as pressure, turbulence, and darkness—demand gradual, controlled navigation to collect scientific data safely. By descending in fractional stages, the drone avoids overwhelming sensors or systems while efficiently mapping and sampling hard-to-reach zones critical to volcanology, geochemistry, and extremophile research.", "Understanding such descent patterns also informs mission planning: technology developers can optimize power use, communication bursts, and sensor activation timing at each phase, ensuring reliability and data integrity.", "### Conclusion", "A research drone descending into a 3,600-meter vent, progressing through 1/4, then 2/5, and finally 1/3 of the remaining depth, has traveled a total of 2,520 meters. This methodical, stage-based approach reflects the precision engineering behind modern exploration drones, enabling safer, more effective vent research in some of Earth’s most extreme environments.", "---\nKeywords: research drone descent, 3,600 meter vent, step-by-step descent, drone navigation, vent exploration, elevation calculation, scientific robotics"]