SOLUTION: It requires 5 hrs for Margaret to paint a building. If she and Sam work together, they can paint the same building in 3 hours. Find the time, in hours, it would take Sam to paint t

Algebra ->  Rate-of-work-word-problems -> SOLUTION: It requires 5 hrs for Margaret to paint a building. If she and Sam work together, they can paint the same building in 3 hours. Find the time, in hours, it would take Sam to paint t      Log On


   

Question 796733: It requires 5 hrs for Margaret to paint a building. If she and Sam work together, they can paint the same building in 3 hours. Find the time, in hours, it would take Sam to paint the building alone.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = time in hrs for Sam to paint building alone
Margaret's rate: ( 1 building ) / ( 5 hrs )
Margaret and Sam together: ( 1 building ) / ( 3 hrs )
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Add their rates to get rate working together
+1%2F5+%2B+1%2Ft+=+1%2F3+
Multiply both sides by +15t+
+3t+%2B+15+=+5t+
+2t+=+15+
+t+=+7.5+
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Sam can paint the building alone in 7.5 hrs
check:
+1%2F5+%2B+1%2Ft+=+1%2F3+
+.2+%2B+1%2F7.5+=+.333+
+.2+%2B+.1333+=+.333+
+.333+=+.333+
OK