Question
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?
Answers
GPT 3.5
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.
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.