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
Here's how to solve this work-rate problem: Step 1: Calculate the total work units required to build the road. The total work is constant regardless of the number of people or hours. We can express work units as (number of people) × (days) × (hours per day). In the first scenario: Number of people (M_1) = 39 Days (D_1) = 12 Hours per day (H_1) = 5 Total Work Units = M_1 × D_1 × H_1 = 39 × 12 × 5 Total Work Units = 39 × 60 = 2340 work units Step 2: Set up the equation for the second scenario. In the second scenario: Number of people (M_2) = 30 Hours per day (H_2) = 6 Days (D_2) = ? (This is what we need to find) The total work units remain the same. Total Work Units = M_2 × D_2 × H_2 2340 = 30 × D_2 × 6 Step 3: Solve for D_2. 2340 = 180 × D_2 D_2 = (2340)/(180) D_2 = (234)/(18) D_2 = 13 So, 30 people working 6 hours a day can complete the work in 13 days. The final answer is 13 days 3 done, 2 left today. You're making progress.