City's Water Resource Management?

📌 CONCEPT: The problem requires us to determine the number of hours for which the reservoirs can supply water at a given rate, which can be solved using the concept of definite integrals to find the volume of water supplied over time.

📐 RULE / FORMULA: Let's assume t be the time in hours. The total volume of water supplied by the reservoirs can be calculated as the sum of the volumes of water supplied from reservoirs A and B, which can be expressed as the integral of the supply rate with respect to time, i.e., ∫ t)dt.

💡 WORKED EXAMPLE: Suppose the total volume of water supplied is 2,00,000 cubic meters from reservoir A and 3,00,000 cubic meters from reservoir B. The supply rate is 800 cubic meters per hour. We can calculate the time 't' for which the reservoirs can supply water as follows:

∫ t)dt = (2,00,000 + 3,00,000) / 800

= 5,00,000 / 800

= 625 hours

⚠️ COMMON MISTAKE: Students often forget to consider the capacity of the reservoirs while solving such problems, which can lead to incorrect results.