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 this work-rate problem: Step 1: Determine the individual work rate of A. A can complete the work in 40 days. So, A's one-day work rate is (1)/(40) of the total work. Step 2: Determine the combined work rate of A and B. A and B together can complete the work in 8 days. So, their combined one-day work rate is (1)/(8) of the total work. Step 3: Set up the equation to find B's work rate. The combined work rate of A and B is the sum of their individual work rates. Let B's one-day work rate be (1)/(T_B), where T_B is the time B takes to complete the work alone. (1)/(40) + (1)/(T_B) = (1)/(8) Step 4: Solve for B's one-day work rate. Subtract A's work rate from the combined work rate: (1)/(T_B) = (1)/(8) - (1)/(40) Find a common denominator, which is 40: (1)/(T_B) = (5)/(40) - (1)/(40) (1)/(T_B) = (5 - 1)/(40) (1)/(T_B) = (4)/(40) (1)/(T_B) = (1)/(10) Step 5: Determine the time B takes to complete the work alone. Since B's one-day work rate is (1)/(10), B will take 10 days to complete the work alone. T_B = 10 days The final answer is 10 days Got more? Send 'em!