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When both painters work together, how much of the job do they complete per hour if one can do it in twelve hours and the other in eight?

  1. 1/24 of the job

  2. 1/12 of the job

  3. 5/24 of the job

  4. 1/5 of the job

The correct answer is: 5/24 of the job

To determine how much of the job the two painters can complete together in one hour, we first need to calculate their individual work rates. The first painter can complete the entire job in twelve hours, which means their rate of work is 1/12 of the job per hour. This comes from taking the whole job (1) and dividing it by the time (12 hours); thus, their contribution per hour is 1/12. The second painter can finish the job in eight hours, giving them a work rate of 1/8 of the job per hour, as this is derived by dividing the whole job (1) by the time taken (8 hours). Now, to find out how much they can complete together in an hour, we add their individual rates: 1/12 (first painter) + 1/8 (second painter) To perform this addition, we need a common denominator. The least common multiple of 12 and 8 is 24. Now, we convert each fraction: 1/12 = 2/24 (by multiplying numerator and denominator by 2) 1/8 = 3/24 (by multiplying numerator and denominator by 3) Adding the two together: 2/24 +