SOLUTION: Mark can clean his fathers office in 30 min. His younger sister Lynn can clean the office in 40 min. How long will it take the two of them together to clean the office?

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Mark can clean his fathers office in 30 min. His younger sister Lynn can clean the office in 40 min. How long will it take the two of them together to clean the office?      Log On


   



Question 754815: Mark can clean his fathers office in 30 min. His younger sister Lynn can clean the office in 40 min. How long will it take the two of them together to clean the office?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Add their rates of cleaning
Mark's rate:
( 1 office cleaned ) / ( 30 min )
Lynn's rate:
( 1 office cleaned ) / ( 40 min )
Let +t+ = the time in minutes for them
to clean the office working together
------------------------------
+1%2F30+%2B+1%2F40+=+1%2Ft+
Multiply both sides by +120t+
+4t+%2B+3t+=+120+
+7t+=+120+
+t+=+17.143+ min
check answer:
+1%2F30+%2B+1%2F40+=+1%2Ft+
+.0333+%2B+.025+=+1%2F17.143+
+.05833+=+.05833+
OK