Greetings,

I have the following problem:

A worker can complete a task two days after another worker does. But if the first worker works for 5 days and after that the second one works for 6 days the task will be completed. How many days would it take for each worker to finish the task alone?

The answer is 10 and 12 and I know how to get to it. However, I have come up with an alternative solution.

Obviously, the task is completed by the workers in 11 days. However, assume the second worker was to replace the first one. Then what the first one did in 5 days, he could do two days faster, or in 3 days. Now, adding that to his 6 original days, we get that the task is completed in 9 days by the second worker working alone, respectively 11 by the first one.

Where am I losing a day?