# SOLUTION: James can stuff 1000 envelopes in 5 hours. Susan can stuff 1000 envelopes in 3 hours. How long will it take to stuff 1000 envelopes if they worked together? answer:it will tak

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 Question 164481: James can stuff 1000 envelopes in 5 hours. Susan can stuff 1000 envelopes in 3 hours. How long will it take to stuff 1000 envelopes if they worked together? answer:it will take 1 7/8 hours to stuff 1,000 envelopes working together need a break down of how my book got 1 7/8 hours to stuff 1,000 envelopes together Found 2 solutions by ptaylor, themathprof:Answer by ptaylor(2052)   (Show Source): You can put this solution on YOUR website!Let x=number of hours it takes with both working together James stuffs at the rate of 1000/5=200 envelopes per hour Susan stuffs at the rate of 1000/3=333.333333 =333 1/3 envelopes per hour Together they stuff at the rate of 200+333.3333=533.3333=533 1/3 envelopes per hour So, our equation to solve is: (533 1/3)*x=1000 divide each side by 533 1/3 x=1.875 hours or 1 7/8 hours--------ans Now we can stay with fractions: x=1000/(533 1/3)=1000/(1600/3)=1000*(3/1600)=3000/1600=30/16=15/8=1 7/8 hr Hope this helps----ptaylor Answer by themathprof(21)   (Show Source): You can put this solution on YOUR website!James can stuff 1000 envelopes in 5 hours. Susan can stuff 1000 envelopes in 3 hours. How long will it take to stuff 1000 envelopes if they worked together? The solution does not depend on the number 1000. It would be solved the same way even if 10 letters were stuffed, or 100,000 letters were stuffed. Think of it as completing a job. James can complete a job 5 hours. Susan can complete the same job in 3 hours. How long will it take to complete the job if they worked together? Let x=amt of hours each will work. Since they're working together, each of their times =x James needs 5 hrs by himself. So each hour he completes 1/5. Susan needs 3 hours by herself, so each hour she completes 1/3 But each don't work 1 hour they work x hours. So,... James completes x/5 Susan completes x/3 Together they complete x/5+x/3 The whole job is 1 x/5+x/3=1 Multiply each term by the LCM=15 to clear fractions 15x/5 +15x/3=15 3x+5x=15 8x=15 x=15/8 x= 1 7/8 hours See more word problems like this worked out step by step in my FREE math911 tutorials. Download, install, activate, ALL FREE from www.math911.com Tell your friends, (and teacher!) Professor Martin Weissman