SOLUTION: Sam can paint the house in 7 days by himself, while Betty can paint the same house in 42 days. How long would it take Sam and Betty to paint the house together?

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Sam can paint the house in 7 days by himself, while Betty can paint the same house in 42 days. How long would it take Sam and Betty to paint the house together?       Log On


   

Question 749866: Sam can paint the house in 7 days by himself, while Betty can paint the same house in 42 days. How long would it take Sam and Betty to paint the house together?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Sam's rate is ( 1 house ) / ( 7 days ) = +1%2F7+
Betty's rate is ( 1 house ) / ( 42 days ) = +1%2F42+
Add their rates to get their rate working together
Let +t+ = their time in days working together
+1%2F7+%2B+1%2F42+=+1%2Ft+
Multiply both sides by +42t+
+6t+%2B+t+=+42+
+7t+=+42+
+t+=+6+
Together it takes them 6 days to paint the house