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
Step 1: Determine the filling rate of Tap A. Tap A fills 10\% of the tank in 1(1)/(2) minutes. 10\% = (10)/(100) = (1)/(10) of the tank. 1(1)/(2) minutes = (3)/(2) minutes. The rate of Tap A is the fraction of the tank filled per minute: Rate_A = (1)/(10) tank(3)/(2) minutes = (1)/(10) × (2)/(3) tankminute = (2)/(30) tankminute = (1)/(15) tankminute Step 2: Determine the emptying rate of Tap B. Tap B empties the entire tank (1 whole tank) in 20 minutes. The rate of Tap B is the fraction of the tank emptied per minute: Rate_B = 1 tank20 minutes = (1)/(20) tankminute Since Tap B empties the tank, its contribution to filling is negative. Step 3: Calculate the combined rate when both taps are open. The combined rate is the filling rate minus the emptying rate: Combined Rate = Rate_A - Rate_B Combined Rate = (1)/(15) - (1)/(20) To subtract these fractions, find a common denominator, which is 60. Combined Rate = (1 × 4)/(15 × 4) - (1 × 3)/(20 × 3) Combined Rate = (4)/(60) - (3)/(60) Combined Rate = (4 - 3)/(60) = (1)/(60) tankminute Step 4: Calculate the time required to fill the tank. If the combined rate is (1)/(60) of the tank per minute, then the time to fill 1 whole tank is: Time = Total Tank CapacityCombined Rate Time = 1 tank(1)/(60) tankminute = 1 × 60 minutes = 60 minutes The time it will take to fill the tank is 60 minutes. That's 2 down. 3 left today — send the next one.