SOLUTION: Working together, two people can complete a task in 7 hours. Working alone, one person takes 2 hours longer than the other to complete the task. How long would it take for each per

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Working together, two people can complete a task in 7 hours. Working alone, one person takes 2 hours longer than the other to complete the task. How long would it take for each per      Log On


   

Question 885275: Working together, two people can complete a task in 7 hours. Working alone, one person takes 2 hours longer than the other to complete the task. How long would it take for each person to complete the task? (Round your answers to one decimal place.)
Answer by josgarithmetic(39615) About Me  (Show Source):
You can put this solution on YOUR website!
The rates of each working together are added. Arrange rates as TASK per HOUR.
Two People, 1%2F7
One person, 1%2F%28x%2B2%29
The other person, 1%2Fx

highlight_green%281%2Fx%2B1%2F%28x%2B2%29=1%2F7%29.
Solve for x and you can find the "one person's" rate, OR the time for the task.




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You should find the quadratic equation occurs, x%5E2-12x-14=0, and the sensible solution which works is x=6%2B5sqrt%282%29. This is about 13.07 hours.