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
Welcome back Duke — missed you this week. Step 1: Identify the given information. We are given that 5 men can clear a bush in 3 hours. We need to find out how many men are required to clear the same bush in (3)/(4) hours. This is an inverse proportion problem, meaning that as the time decreases, the number of men must increase. Let M_1 be the initial number of men and T_1 be the initial time. Let M_2 be the new number of men and T_2 be the new time. Given: M_1 = 5 men T_1 = 3 hours T_2 = (3)/(4) hours Step 2: Set up the inverse proportionality equation. For inverse proportionality, the product of men and time remains constant: M_1 T_1 = M_2 T_2 Step 3: Substitute the known values into the equation. 5 men × 3 hours = M_2 × (3)/(4) hours Step 4: Solve for M_2. 15 = M_2 × (3)/(4) To find M_2, divide both sides by (3)/(4): M_2 = (15)/(3)4 M_2 = 15 × (4)/(3) M_2 = (15 × 4)/(3) M_2 = (60)/(3) M_2 = 20 Therefore, 20 men can clear the bush in (3)/(4) hours. The number of men required is 20 men. Send me the next one 📸