SOLUTION: Alan can sweep a porch in 9 minutes. Bill can sweep the same porch in 14 minutes. How long will it take them to sweep the same porch together? The answer is 5.48 minutes. I get 5.7

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Alan can sweep a porch in 9 minutes. Bill can sweep the same porch in 14 minutes. How long will it take them to sweep the same porch together? The answer is 5.48 minutes. I get 5.7      Log On


   

Question 937976: Alan can sweep a porch in 9 minutes. Bill can sweep the same porch in 14 minutes. How long will it take them to sweep the same porch together? The answer is 5.48 minutes. I get 5.75 minutes. How do I set up the problem?
Thank You
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
Alan and Bill. Let their times to do one job alone be A and B. Their individual rates are then 1/A and 1/B in unit of PORCHES per MINUTE.

The amount of the work to be done using Alan and Bill working at the same time together is 1, for ONE PORCH or ONE JOB.

Let t be the time in minutes for Alan and Bill to sweep the one porch.

%281%2FA%2B1%2FB%29t=1

Assumption may be that you just made a mistake in your steps.

%28B%2FAB%2BA%2FAB%29t=1

%28%28B%2BA%29%2F%28AB%29%29t=1

highlight%28t=%28AB%29%2F%28A%2BB%29%29, excuse the simple skipped step.

Plug in the given values, A=9, B=14, and evaluate t.
Intermediate step should be 126%2F23.
highlight%285%2611%2F23%29
5.48