Before the library is remodeled, all of the books must be 
packed in boxes. Working alone, it will take Gail 15 
workdays to do the packing. It would take Rob 18 workdays. 
How long will it take them working together?

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Let the answer be x workdays

>>>...it will take Gail 15 workdays to do the packing...<<

Therefore in 1 workday Gail can do 1/15 of the packing.

Therefore in x workdays Gail can do x/15 of the packing.

>>>...It would take Rob 18 workdays (ro do the packing)...<<

Therefore in 1 workday Bob can do 1/18 of the packing.

Therefore in x workdays Bob can do x/18 of the packing.

So the x/15 of the packing Gail can do PLUS the x/18 of
the packing Bob can do must total 1 packing:

 

Write the 1 as 

 

Put parentheses around every term:

 

Multiply through by LCD = 



All that's left after canceling 
and multiplying is:
 








Edwin