3 workers can do a job in 12 days.2 of the workers work twice as first as the third.How long would it take one of faster workers to do the job alone?
To solve this problem, let's break it down step by step:
1. Determine the efficiency ratio: We know that 2 of the workers work twice as fast as the third worker. Therefore, the efficiency ratio is 2:1.
2. Calculate the combined work rate of the workers: Since 3 workers can complete the job in 12 days, we can assume that their combined work rate is 1 job per (3 workers * 12 days) = 1/36 jobs per day.
3. Calculate the individual work rate of the third worker: Since the first two workers work twice as fast as the third worker, the third worker's work rate is 1/2 of the combined work rate. Therefore, the third worker's work rate is 1/36 jobs per day * 1/2 = 1/72 jobs per day.
4. Calculate the individual work rate of the faster workers: Since the first two workers work twice as fast as the third worker, their combined work rate is 2/3 of the combined work rate of all three workers. Therefore, their combined work rate is 2/3 * 1/36 jobs per day = 2/108 = 1/54 jobs per day.
5. Determine how long it would take one of the faster workers: To find the time it takes for one worker to complete the job alone, we need to calculate the reciprocal of their work rate. Therefore, one of the faster workers would take 54 days to complete the job alone.
So, it would take one of the faster workers 54 days to do the job alone.