SOLUTION: A person worked 12 hours to clean the house. Another person worked 15 hours to clean the same house. How long do they work if they work together?

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Question 617160: A person worked 12 hours to clean the house. Another person worked 15 hours to clean the same house. How long do they work if they work together?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Add their rates of working
person 1: ( 1 house ) / ( 12 hrs )
person 2: ( 1 house ) / ( 15 hrs )
Let +t+ = the time in hours for them
to clean house together
+1%2F12+%2B+1%2F15+=+1%2Ft+
Multiply both sides by +60t+
+5t+%2B+4t+=+60+
+9t+=+60+
+t+=+6.667+ hrs
Note that +.667+ hrs is +40+ min
Working together, it takes them 6 hrs and 40 min