SOLUTION: Working together, Jenny and Natalie can assemble a desk in 42/13 hours. Working alone Jenny could have done it in 7 hours. How long would it take Natalie working alone? hours.

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Question 1194386: Working together, Jenny and Natalie can assemble a desk in 42/13 hours. Working alone Jenny could have done it in 7 hours. How long would it take Natalie working
alone?
hours.
Found 4 solutions by math_tutor2020, ikleyn, greenestamps, MathTherapy:
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!

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: 6 hours

Answer by ikleyn(52802)   (Show Source):
You can put this solution on YOUR website!
.
Working together, Jenny and Natalie can assemble a desk in 42/13 hours.
Working alone Jenny could have done it in 7 hours.
How long would it take Natalie working alone?
~~~~~~~~~~~~~~

Since J and N can do the job in hours, their combined rate of work is . It means that they can do of the entire job in one hour, working together. Jenny's individual rate of work is of the job per hour. Hence, Natalie's individual rate of work is this difference - = = = = of the job per hour. It means that Natalie can do the entire job in 6 hours, working alone. ANSWER

Solved.

---------------

It is a standard and typical joint work problem.

There is a wide variety of similar solved joint-work problems with detailed explanations in this site. See the lessons
    - Using Fractions to solve word problems on joint work
    - Solving more complicated word problems on joint work
    - Selected joint-work word problems from the archive

Read them and get be trained in solving joint-work problems.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook under the topic
"Rate of work and joint work problems" of the section "Word problems".

Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.

Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!

You should understand the formal algebraic solutions shown by the other tutors and be able to use them to solve similar problems.

But if you encounter this kind of problem often (e.g., you are a student on a school math team), you can use this standard shortcut:

If the times required for two workers to do a job alone are a and b, then the time required for them to do the job working together is (ab)/(a+b).

In this problem we know the number of hours for one of the workers working alone is 7 and the number of hours for the two working together is 42/13, so

ANSWER: Natalie working alone would take 6 hours to do the job.

Answer by MathTherapy(10552)   (Show Source):
You can put this solution on YOUR website!

Working together, Jenny and Natalie can assemble a desk in 42/13 hours. Working alone Jenny could have done it in 7 hours. How long would it take Natalie working
alone?
hours.

Let time Natalie takes, alone, be N Then Natalie can do of job in 1 hour Since Jenny takes 7 hours alone, Jenny can do of job in 1 hour With both completing the job in , we get the following: 42 + 6N = 13N ------ Multiplying by LCD, 42N 42 = 7N Time Natalie takes, alone, or