This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Hey kesharoli2024, good to see you again. Here's how to solve the problem: Step 1: Determine the individual rates of each pipe. Pipe P fills the tank in 5 hours, so its filling rate is (1)/(5) of the tank per hour. Pipe Q fills the tank in 6 hours, so its filling rate is (1)/(6) of the tank per hour. Pipe R empties the tank in 12 hours, so its emptying rate is -(1)/(12) of the tank per hour. Step 2: Calculate the combined rate of all three pipes working together. The combined rate is the sum of the individual rates, with emptying rates being negative. Combined Rate = (1)/(5) + (1)/(6) - (1)/(12) Step 3: Find a common denominator and sum the fractions. The least common multiple (LCM) of 5, 6, and 12 is 60. Combined Rate = (1 × 12)/(5 × 12) + (1 × 10)/(6 × 10) - (1 × 5)/(12 × 5) Combined Rate = (12)/(60) + (10)/(60) - (5)/(60) Combined Rate = (12 + 10 - 5)/(60) Combined Rate = (22 - 5)/(60) Combined Rate = (17)/(60) tank/hour Step 4: Calculate the total time taken to fill the tank. The time taken is the reciprocal of the combined rate. Time = (1)/(Combined Rate) Time = (1)/(17)60 Time = (60)/(17) hours The tank will be filled in (60)/(17) hours. The final answer is (60)/(17) hours Send me the next one 📸