Answer :
Final answer:
To find out how many days 15 senior technicians and 20 junior technicians will take to complete the work, one calculates the work done by each technician per day and then sums the efforts. Upon calculation, it is found that they would take 30 days to complete the work together, which does not match any of the given options.
Explanation:
The question is about work rate and calculating the combined effort of two groups of workers with different efficiencies. To solve this, we will first find out how much work one senior technician and one junior technician can do in one day. Then, we will calculate the total daily work output for 15 senior technicians and 20 junior technicians and determine how many days it would take for them to complete the work.
Let the total work be represented by the variable W. If 45 senior technicians take 20 days to complete the work, then the work done by one senior technician in a day would be W / (45 * 20). Similarly, for 60 junior technicians, the work done by one junior technician in a day would be W / (60 * 20).
Now, 15 senior technicians and 20 junior technicians will work together:
- Work done by 15 senior technicians in one day = 15 * (W / (45 * 20))
- Work done by 20 junior technicians in one day = 20 * (W / (60 * 20))
Combined daily work output:
15 * (W / (45 * 20)) + 20 * (W / (60 * 20)) = W / 20
Calculation:
15 * (W / (45 * 20)) + 20 * (W / (60 * 20)) = W / 60 + W / 60 = (2W) / 60
Therefore, they work at a rate of (2W) / 60 per day. To complete one unit of work W, it will take them W / ((2W) / 60) days, which simplifies to 30 days.
The answer is not listed in the multiple-choice options provided, indicating there might be a mistake in the given options or in the calculations made. With the calculations above, 30 days would be the correct answer for the combined work rate of 15 senior and 20 junior technicians to complete the job.
