Let's denote the time it takes the repairman to fix one pair of shoes by himself as R hours, and the time it takes the assistant to fix one pair of shoes by himself as A hours.
We know that the assistant takes twice as long as the repairman, so A = 2R.
In one hour, working together, they can fix 16 pairs of shoes in 8 hours. This means that in one hour, they can fix 2 pairs of shoes.
So, the repairman can fix 1 pair of shoes in R hours and the assistant can fix 1 pair of shoes in A hours. Therefore, in one hour, the repairman can fix 1/R pairs of shoes and the assistant can fix 1/A pairs of shoes.
Given that in one hour, they can fix 2 pairs of shoes together, we can write the equation:
1/R + 1/A = 1/8 + 1/16
1/R + 1/2R = 1/8 + 1/16
3/2R = 3/16
R = 2/16
R = 1/8
Therefore, it takes the repairman 8 hours to fix one pair of shoes by himself.
A shoe repairman is working with his assistant, who takes twice as long to repair a pair of shoes. Together they can fix 16 pairs of shoes in an eight-hour day. How long does it take the repairman to fix one pair of shoes by himself?
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