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 rubbydiaz373 — let's get this done. Step 1: Determine the individual work rates. The rate of work is the reciprocal of the time taken to complete the job. Worker 1's rate: R_1 = (1)/(12) job/hour Worker 2's rate: R_2 = (1)/(8) job/hour Step 2: Calculate their combined work rate. When working together, their rates add up. R_combined = R_1 + R_2 R_combined = (1)/(12) + (1)/(8) To add these fractions, find a common denominator, which is 24. R_combined = (1 × 2)/(12 × 2) + (1 × 3)/(8 × 3) R_combined = (2)/(24) + (3)/(24) R_combined = (2+3)/(24) R_combined = (5)/(24) job/hour Step 3: Calculate the total time taken to complete the job together. The total time is the reciprocal of the combined rate. T_total = (1)/(R_combined) T_total = (1)/(5)24 T_total = (24)/(5) hours To express this in hours and minutes: T_total = 4 (4)/(5) hours Convert the fractional part to minutes: (4)/(5) hours × 60 minutes/hour = 4 × 12 minutes = 48 minutes So, the total time is 4 hours and 48 minutes. The total time it will take them to finish the job altogether is 4 hours 48 minutes. Send me the next one 📸