Answer: 80 days
Explanation:
Let's break down the problem step by step:
1. Six experienced workers can finish the job in 120 days, so their combined work rate is 1 job per 120 days.
2. When three new workers are added, they work at half the rate of the experienced workers. Therefore, the combined work rate of three new workers is 1 job per (2 * 120) days, which is 1 job per 240 days.
Now, you want to find out how long it would take for the six experienced workers and the three new workers to finish the job together. Let's call this time "t" (measured in days).
The combined work rate of all nine workers is the sum of the work rates of the six experienced workers and the three new workers:
1/120 (work rate of experienced workers) + 1/240 (work rate of new workers) = 1/t (combined work rate)
To solve for "t," you can find a common denominator and add the fractions:
(2/240) + (1/240) = 1/t
(3/240) = 1/t
Now, you can simplify the left side of the equation:
(1/80) = 1/t
To isolate "t," take the reciprocal of both sides of the equation:
t = 80 days
So, it would take the six experienced workers and the three new workers 80 days to finish the job together.