Question 1194386
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Let's say this desk has 42 pieces. I'm picking 42 because it will cancel out later on with the other 42 from 42/13.


Let x be the combined rate of Jenny and Natalie working together. 


The idea is to multiply the number of hours they work together (42/13) with their combined rate (x) and that will tell us how many pieces they're able to assemble (42)


So,
(number of hours)*(pieces per hour) = number of pieces
(42/13)*x = 42
x = 42*(13/42)
x = 13


At this point, it's probably more clear why I picked 42
The cancellation happens at the last step. 


If there are 42 pieces total, then their combined rate is 13 pieces per hour.


Another reason why I picked 42 is because it's a multiple of 7.
If Jenny works alone and she takes 7 hours, then her rate is 42/7 = 6 pieces per hour.
This leaves Natalie's rate to be 13 - 6 = 7 pieces per hour.


Therefore, if Natalie works alone, then she will take 42/7 = 6 hours.


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Here's an alternative approach using the standard method to solve rate of work problems.


n = number of hours Natalie needs if she works alone


1/n = Natalie's rate in jobs per hour
In other words, she does 1 job per n hours


Also, Jenny needs 7 hours, so her rate is 1/7 of a job per hour.


1/n + 1/7 = their combined rate in jobs per hour
That simplifies to (7+n)/(7n)


If they work together and get the job done in 42/13 hours, then their rate must be 13/42 jobs per hour.


Set this equal to the (7+n)/(7n) and let's solve for n.


(7+n)/(7n) = 13/42
42(7+n) = 7n*13
294+42n = 91n
91n-42n = 294
49n = 294
n = 294/49
n = 6


Natalie can get the job done in 6 hours if she works alone.


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Answer: <font color=red>6 hours</font>
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