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
Morning rahmahangel223😼 — let's get this done. Here's the solution to the problem: Given: Tank capacity = 9600 litres Tap R fills the tank in 9 minutes. Tap S fills the tank in 12 minutes. Tap T empties the tank in 6 minutes. a) How much is put in the tank by tap R in one minute? Step 1: Calculate the rate of tap R. Tap R fills 9600 litres in 9 minutes. Rate of R = Total capacityTime taken by R = 9600 litres9 minutes Rate of R = 1066.67 litres/minute Tap R puts approximately 1066.67 litres into the tank in one minute. 1066.67 litres b) How much is drawn from the tank by tap T? Step 1: Calculate the rate of tap T. Tap T empties 9600 litres in 6 minutes. Rate of T = Total capacityTime taken by T = 9600 litres6 minutes Rate of T = 1600 litres/minute Tap T draws 1600 litres from the tank in one minute. 1600 litres c) How many litres of water tap R and Tap S pour into the tank in one minute? Step 1: Calculate the rate of tap S. Tap S fills 9600 litres in 12 minutes. Rate of S = Total capacityTime taken by S = 9600 litres12 minutes Rate of S = 800 litres/minute Step 2: Calculate the combined rate of tap R and tap S. Combined rate (R+S) = Rate of R + Rate of S Combined rate (R+S) = 1066.67 litres/minute + 800 litres/minute Combined rate (R+S) = 1866.67 litres/minute Tap R and Tap S pour approximately 1866.67 litres into the tank in one minute. 1866.67 litres d) How long will it take to fill the tank if all taps are left open at the same time? Step 1: 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 R + Rate of S - Rate of T Net rate = 1066.67 litres/minute + 800 litres/minute - 1600 litres/minute Net rate = 1866.67 litres/minute - 1600 litres/minute Net rate = 266.67 litres/minute Step 2: Calculate the time taken to fill the tank. Time = Total capacityNet rate Time = 9600 litres266.67 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 Send me the next one 📸