# Math Help - Word problem

1. ## Word problem

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?

2. Originally Posted by Logic
A worker can complete a task two days after another worker does.
This is poorly worded. It should be reworded so that it is more likely to be understood as meaning that the same task can be completed by the two workers, but working alone, one would take two days longer.

Then what the first one did in 5 days, he could do two days faster, or in 3 days.
No good. The whole job is a two-day spread. Why would part of the job also be a two-day spread?

Try this:

n = Number of days for the faster worker to complete the job.
m = Number of days for the slower worker to complete the job.

Reality therapy.

The fast worker can complete 1/n of the task in 1 day. In 2 days, 2/n of the task is done... In n days, n/n of the task, or the whole task, is accomplished.

Now ponder this:

$\frac{5}{n} + \frac{6}{m} = 1$

What does it mean?

We also know that m = n+2

Note: If you are REALLY careful, you should get two solutions. One is no good.

Let's see what you get.