SOLUTION: HI, i need help with the last part. I understood most of it but i don't know how to get the final result. 1. It takes Mom, Dad and Isabel two hours to shovel their driveway a

Algebra ->  Rational-functions -> SOLUTION: HI, i need help with the last part. I understood most of it but i don't know how to get the final result. 1. It takes Mom, Dad and Isabel two hours to shovel their driveway a      Log On


   



Question 1182436: HI, i need help with the last part. I understood most of it but i don't know how to get the final result.

1. It takes Mom, Dad and Isabel two hours to shovel their driveway after a snow storm. If Dad worked alone, it would take him 4 hours to shovel the entire driveway by himself. If Isabel worked alone, it would take her twice as long as Dad. How long would it take Mom to shovel the driveway herself?
- (Use the prime factorization of the known denominators to rewrite each term with a common denominator.)
Show your work

Answer by ikleyn(52800) About Me  (Show Source):
You can put this solution on YOUR website!
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HI, i need help with the last part. I understood most of it but i don't know how to get the final result.
1. It takes Mom, Dad and Isabel two hours to shovel their driveway after a snow storm.
If Dad worked alone, it would take him 4 hours to shovel the entire driveway by himself.
If Isabel worked alone, it would take her twice as long as Dad. How long would it take Mom to shovel the driveway herself?
- (Use the prime factorization of the known denominators to rewrite each term with a common denominator.)
Show your work
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The three participants make  1%2F2  of the job per hour (from the condition). It is their combined rate of work.


Dad makes  1%2F4  of the job per hour, working alone (given).


Isabel makes  1%2F8  of the job per hour, working alone (from the condition).


It means that Mom's rate of work is  1%2F2 - 1%2F4 - 1%2F8 = 4%2F8 - 2%2F8 - 1%2F8 = 1%2F8  of the job per hour.


Hence, Mom will make the entire job in 8 hours.  


ANSWER.  Mom will make the entire job in 8 hours, working alone.

Solved.

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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.