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
You're on a roll — here's the solution to the problem: Given: Tank capacity = 7200 litres Tap A fills the tank in 9 minutes. Tap B fills the tank in 12 minutes. Tap C empties the tank in 6 minutes. a) What capacity of water is put in the tank by A in one minute? Step 1: Calculate the rate of tap A. Tap A fills 7200 litres in 9 minutes. Rate of A = Total capacityTime taken by A = 7200 litres9 minutes Rate of A = 800 litres/minute Tap A puts 800 litres into the tank in one minute. 800 litres b) What capacity will be put in the tank by tap B after one minute? Step 1: Calculate the rate of tap B. Tap B fills 7200 litres in 12 minutes. Rate of B = Total capacityTime taken by B = 7200 litres12 minutes Rate of B = 600 litres/minute Tap B puts 600 litres into the tank in one minute. 600 litres c) How long will it take to fill the tank if all taps are open at the same time? Step 1: Calculate the rate of tap C. Tap C empties 7200 litres in 6 minutes. Rate of C = Total capacityTime taken by C = 7200 litres6 minutes Rate of C = 1200 litres/minute Step 2: Calculate the net filling rate when all taps are open. The net rate is the sum of filling rates minus the emptying rate. Net rate = Rate of A + Rate of B - Rate of C Net rate = 800 litres/minute + 600 litres/minute - 1200 litres/minute Net rate = 1400 litres/minute - 1200 litres/minute Net rate = 200 litres/minute Step 3: Calculate the time taken to fill the tank. Time = Total capacityNet rate Time = 7200 litres200 litres/minute Time = 36 minutes It will take 36 minutes to fill the tank if all taps are left open at the same time. 36 minutes Drop the next question.