SOLUTION: A crew will arrive in 1 week and begin filming a city for a movie. The mayor wants to clean the streets. 2 teams are available. Team 1 will take 200 hours to complete. Team 2 will

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A crew will arrive in 1 week and begin filming a city for a movie. The mayor wants to clean the streets. 2 teams are available. Team 1 will take 200 hours to complete. Team 2 will       Log On


   

Question 965904: A crew will arrive in 1 week and begin filming a city for a movie. The mayor wants to clean the streets. 2 teams are available. Team 1 will take 200 hours to complete. Team 2 will take 500 hours to complete. How long will it take if both teams work together?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = time in hours for both teams
working together to complete job
------------------
Add their rates of working to get their
rate working together:
[ 1 job ] / [ 200 hrs ] + [ 1 job ] / [ 500 hrs ] = [ 1 job ][ / [ t hrs ]
+1%2F200+%2B+1%2F500+=+1%2Ft+
Multiply both sides by +1000t+
+5t+%2B+2t+=+1000+
+7t+=+1000+
+t+=+142.86+
Working together, it will take them
142.86 hrs to finish
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check:
+1%2F200+%2B+1%2F500+=+1%2Ft+
+.005+%2B+.002+=+1%2F142.86+
+.007+=+.0069998+
error due to rounding off -OK