Three workers, X, Y, and Z, can complete a certain job in 10 days, 12 days, and 15 days, respectively. Determine the number of days required for them to complete the job when they work together.
4 days
To determine the number of days required for workers X, Y, and Z to complete the job together, we use the concept of work and time, specifically the formula for combined work rate.
Step 1: Determine the work rate of each worker.
- Worker X can complete the job in 10 days, so X's work rate is \(\frac{1}{10}\) of the job per day.
- Worker Y can complete the job in 12 days, so Y's work rate is \(\frac{1}{12}\) of the job per day.
- Worker Z can complete the job in 15 days, so Z's work rate is \(\frac{1}{15}\) of the job per day.
Step 2: Calculate the combined work rate.
The combined work rate when all workers work together is the sum of their individual work rates:
\(\frac{1}{10} + \frac{1}{12} + \frac{1}{15}\)
To add these fractions, we need a common denominator. The least common multiple of 10, 12, and 15 is 60.
Convert each work rate to have a denominator of 60:
- \(\frac{1}{10} = \frac{6}{60}\)
- \(\frac{1}{12} = \frac{5}{60}\)
- \(\frac{1}{15} = \frac{4}{60}\)
Add these together:
\(\frac{6}{60} + \frac{5}{60} + \frac{4}{60} = \frac{15}{60} = \frac{1}{4}\)
Step 3: Calculate the time to complete the job together.
Since their combined work rate is \(\frac{1}{4}\), they can complete \(\frac{1}{4}\) of the job in one day. Therefore, they will complete 1 whole job in:
\(4 \text{ days}\)
Thus, the correct answer is 4 days.
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