One carpenter can complete a kitchen in 10 days. With the help of another carpenter, they can do the job together in 5 days. How long would it take the second carpenter if he worked alone?
Let's denote the rate at which the first carpenter works as x kitchens per day. Therefore, the first carpenter can complete the kitchen in 1/10 days.
When the second carpenter joins him, the combined rate at which they work is x + y kitchens per day, and they can complete the kitchen in 1/5 days.
Using the formula Rate x Time = Work, we can set up the following equations:
First carpenter: x * 10 = 1
Combined rate: (x + y) * 5 = 1
From the first equation, we have x = 1/10 = 0.1
Substitute x = 0.1 into the second equation:
(0.1 + y) * 5 = 1
0.5 + 5y = 1
5y = 0.5
y = 0.1
Therefore, the second carpenter's rate of completing the kitchen is 0.1 kitchens per day, and it would take him 10 days to complete the kitchen alone.