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Ten workers perform one job in five days 
20070821 

From Kenneth: If ten workers perform one job in 5 days, one person performs one job in how many days?
Here is the calculation that I used:
(10 workers X 1 job X 5 days)/(1 person X 1 job X ? days)
The above equals 50/1, and the answer is 50 days because 50/1 = 50. In this calculation I can determine any number of workers or days if the number of jobs remains the same as that in the group of factors from the numerator (10 workers X 1 job X 5 days), that is 1 job. Here is another example to help clarify: (10 workers X 1 job X 5 days)/(? workers X 1 job X 10 days) This equals 50/10. The answer is 5 workers. So, if 10 workers can perform 1 job in 5 days, 5 workers can perform 1 job in 10 days.
Now, if I replace "1 job" from (10 workers X 1 job X 5 days) with a different number, for example, 4 jobs, this amount will prevent the calculation from producing the correct answer.
Here is an example: (10 workers X 1 job X 5 days)/(10 workers X 4 jobs X ? days) Mathematically, the calculation works, but the answer, 1.25 days, is not correct, if I'm not mistaken. If 10 workers can perform 1 job in 5 days, they cannot, by working at the same rate, perform 4 jobs in 1.25 days.
Can you explain, with a simple explanation, why the number representing the jobs in this calculation needs to be the same in the group of factors in both the numerator and in the denominator in order to provide the correct answer? Answered by Harley Weston. 


