Answer :
Final answer:
15 senior technicians and 20 junior technicians will take 30 days to complete the repair of the truck, None of the options are correct.
Explanation:
To solve the problem, we have to find the combined rate of work of 15 senior technicians and 20 junior technicians given that 45 senior technicians or 60 junior technicians can repair a truck in 20 days. First, we need to determine the rate at which 1 senior technician and 1 junior technician can repair the truck.
Let's assume the total work needed to repair the truck is represented by W. The rate of work of the senior technicians is W/20 days for 45 senior technicians, which simplifies to (W/900) per day for 1 senior technician. Similarly, the rate of work of the junior technicians is W/20 days for 60 junior technicians, giving us (W/1200) per day for 1 junior technician.
Now, if we have 15 senior technicians and 20 junior technicians, their combined daily work rate would be (15 * W/900) + (20 * W/1200). Simplifying this gives us (W/60) + (W/60), which is (W/30) per day. This means that together, they do 1/30 of the work each day.
The important part is to calculate how many days it takes to complete 1 unit of work at the rate of 1/30 per day. The calculation is straightforward: 1 divided by 1/30 equals 30 days.
Therefore, 15 senior technicians and 20 junior technicians will take 30 days to complete the repair of the truck, which is not listed among the supplied options (a) 22 days, (b) 24 days, (c) 26 days, or (d) 28 days.
