Final answer:
To solve this problem, we use the concept of work rate and set up a proportion to find the number of days it would take the new crew to complete the same job.
Step-by-step explanation:
To solve this problem, we can use the concept of work rate. The work rate is the amount of work done per unit of time. In this case, we can consider the work rate of the 12 carpenters to be 1 house every 6 days.
If we increase the number of carpenters by 2, the new crew would have 14 carpenters working. So their work rate would be 14 carpenters completing 1 house in a certain number of days.
Using the concept of work rate, we can set up a proportion: 12 carpenters / 6 days = 14 carpenters / x days
Cross-multiplying, we can solve for x: 12x = 6*14 => x = 6*14/12 = 7 days. So the new crew of 14 carpenters would be able to complete the same job in 7 days.