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Answer :
Final answer:
To find the number of days 15 senior technicians and 20 junior technicians will take to repair a truck, we calculate their combined work rate based on the given rates for 45 senior technicians or 60 junior technicians. The calculation shows these technicians will complete the work in 30 days.So,the correct answer c. 30.
Explanation:
The question asks how many days it will take for 15 senior technicians and 20 junior technicians to repair a truck if 45 senior technicians or 60 junior technicians can do the same job in 20 days. To solve this problem, we first find the amount of work done by the technicians in one day, which is referred to as the work rate. We then calculate the combined work rate of 15 senior technicians and 20 junior technicians to find the total time required to complete the work.First, we find the work rate of 45 senior technicians which is 1/20 of the truck per day since they complete 1 truck in 20 days. Similarly, 60 junior technicians also have a work rate of 1/20 of the truck per day. Therefore, the work rate of 1 senior technician is 1/(45*20) and of 1 junior technician is 1/(60*20).To find the combined work rate, we calculate:
- 15 senior technicians: 15 * 1/(45*20)
- 20 junior technicians: 20 * 1/(60*20)
Add these two rates together to get the total work rate for 15 senior technicians and 20 junior technicians. Finally, to find the number of days needed, we take the reciprocal of this total work rate.After calculations, we find that 15 senior technicians and 20 junior technicians will complete the work in 30 days, making the correct answer c. 30.
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