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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 of the job per hour (from the condition). It is their combined rate of work.
Dad makes of the job per hour, working alone (given).
Isabel makes of the job per hour, working alone (from the condition).
It means that Mom's rate of work is - - = - - = 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.