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
Here's how to solve the problem using inverse proportion: The total amount of "work" (filling the tank) is constant. This means the number of taps multiplied by the time taken is constant. Let N be the number of taps and T be the time in minutes. So, N × T = constant. Given: N_1 = 3 taps, T_1 = 54 minutes. The constant work is 3 taps × 54 minutes = 162 tap-minutes. a) 9 taps Step 1: Set up the inverse proportion equation. Let T_2 be the time taken by 9 taps. N_1 T_1 = N_2 T_2 3 taps × 54 minutes = 9 taps × T_2 Step 2: Calculate the total work units. 3 × 54 = 162 tap-minutes Step 3: Solve for T_2. 162 = 9 × T_2 T_2 = (162)/(9) T_2 = 18 minutes It will take 9 taps 18 minutes to fill the tank. b) 12 taps Step 1: Set up the inverse proportion equation. Let T_3 be the time taken by 12 taps. N_1 T_1 = N_3 T_3 3 taps × 54 minutes = 12 taps × T_3 Step 2: Use the total work units calculated previously. 162 tap-minutes = 12 taps × T_3 Step 3: Solve for T_3. T_3 = (162)/(12) T_3 = (81)/(6) T_3 = (27)/(2) T_3 = 13.5 minutes It will take 12 taps 13.5 minutes to fill the tank. Send me the next one 📸