**Quote:**

both work one after another

A reasonable test-taker might interpret this information as follows:

If Adam works one day, then Ben must work the next day.

Earlier posts suggest that a different interpretation is intended.

I believe that the following clarifies the intent of the problem:

**Quote:**

Adam can do a job in 10 workdays. Ben's speed is twice Adam's speed. Every workday either Adam or Ben works but not both. If the job in completed in exactly 7 workdays, what percent of the job is produced by Adam?

(A) 67%

(B) 60%

(C) 50%

(D) 40%

(E) 33%

Let the job = 10 units.

Since Adam takes 10 days to complete the 10-unit job, Adam's rate = \(\frac{w}{t} = \frac{10}{10} = 1\) unit per day.

Since Ben is twice as fast as Adam, Ben's rate = 2 units per day.

For the 10-unit job to be completed in exactly 7 days, only one case is possible:

Adam works at his rate of 1 unit per day for 4 days, producing a total of 4 units.

Ben works at his rate of 2 units per day for 3 days, producing a total of 6 units.

Thus:

\(\frac{Work-by-Adam}{Total-work} = \frac{4}{10} = 40\)%.

An algebraic way to determine the number of days worked by Adam:

Let \(a=\) Adam's number of days and \(b=\) Ben's number of days.

Since Adam produces 1 unit per day, Ben produces 2 units per day, and a total of 10 units are produced, we get:

\(a+2b=10\)Since a total of 7 days are worked, we get:

\(a+b=7\)

\(2a+2b=14\)Subtracting the red equation from the blue equation, we get:

\((2a+2b)-(a+2b) = 14-10\)

\(a=4\)

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