Answer :
Final answer:
15 senior technicians and 20 junior technicians will take 30 days to repair the truck, calculated by determining the combined working rate of both types of technicians and solving for the number of days needed.
Explanation:
The question asks us to calculate how many days 15 senior technicians and 20 junior technicians will take to repair a truck, given that 45 senior technicians or 60 junior technicians can do the same job in 20 days.
First, we determine the rate at which the senior and junior technicians work. Assuming each senior technician has the same efficiency:
- 45 senior technicians can repair the truck in 20 days, so the combined rate of 45 seniors is 1 truck per 20 days.
Therefore, 1 senior technician repairs 1/45 of a truck in 20 days. Similarly, for the junior technicians:
- 60 junior technicians can repair a truck in 20 days, meaning the combined rate of 60 juniors is also 1 truck per 20 days.
Consequently, 1 junior technician repairs 1/60 of a truck in 20 days.
Next, we'll calculate the rate for 15 senior technicians and 20 junior technicians:
- 15 senior technicians would repair 15/45 = 1/3 of a truck in 20 days.
- 20 junior technicians would repair 20/60 = 1/3 of a truck in 20 days.
Combine their rates to find the total rate:
- 1/3 + 1/3 = 2/3 of a truck in 20 days is repaired by the combination of 15 seniors and 20 juniors.
To find the number of days (D) to repair one truck with the combined team, set up the proportion:
- (2/3 truck)/(20 days) = (1 truck)/D
Cross-multiply and solve for D:
- 2/3 * D = 20
- D = 20 / (2/3)
- D = 20 * 3/2
- D = 30 days
So, 15 senior technicians and 20 junior technicians will complete the work in 30 days.
