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?

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

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