Question

If the first painter can do the entire job in twelve hours and the second painter can do it in eight hours, then (this here is the trick!) the first guy can do 1/12 of the job per hour, and the second guy can do 1/8 per hour. How much then can they do per hour if they work together?

Answer 1

The combined hourly productivity of the two painters is 5/24 of the job. Add the individual rates of 1/12 and 1/8, which results in a combined rate of 5/24 when they work together.

Step-by-step explanation:

When two painters work together, their combined productivity per hour is the sum of their individual productivities. The first painter can complete 1/12 of the job per hour, and the second painter can complete 1/8 of the job per hour. To calculate their combined work rate, you simply add these two rates together:

1/12 of the job per hour (first painter) + 1/8 of the job per hour (second painter) = 5/24 of the job per hour (combined).

To perform this calculation, you need to find a common denominator, which is 24 in this case, and then add the two fractions: (2/24) + (3/24) = 5/24. This means that if they work together, the two painters can complete 5/24 of the painting job every hour.

To find out how much work the two painters can do per hour when working together, we need to add up their individual rates of work. The first painter can do 1/12 of the job per hour, and the second painter can do 1/8 per hour. So, together they can do:

1/12 + 1/8 = (2/24) + (3/24) = 5/24

Therefore, when working together, the two painters can do 5/24 of the job per hour.