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:
\((2a+2b)-(a+2b) = 14-10\)
\(a=4\)