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
Step 1: Determine the time B takes to complete the work. A is twice as efficient as B. This means A takes half the time B takes to complete the same work. Given that A finishes the work in 60 days. Let D_A be the number of days A takes and D_B be the number of days B takes. D_A = 60 days Since A is twice as efficient as B, B will take twice as long as A. D_B = 2 × D_A D_B = 2 × 60 days D_B = 120 days Step 2: Calculate the combined work rate of A and B. The work rate of A is (1)/(D_A) per day. The work rate of B is (1)/(D_B) per day. Combined work rate = Work rate of A + Work rate of B Combined work rate = (1)/(60) + (1)/(120) To add these fractions, find a common denominator, which is 120. Combined work rate = (2)/(120) + (1)/(120) Combined work rate = (2+1)/(120) Combined work rate = (3)/(120) Combined work rate = (1)/(40) work per day Step 3: Find the number of days A and B take to finish the work together. The number of days taken to finish the work together is the reciprocal of their combined work rate. Days together = (1)/(Combined work rate) Days together = (1)/(1)40 Days together = 40 days The correct option is A. The final answer is 40 days.