SOLUTION: Marie Just on and Danny are working on their group project. If they work together they can finish it in 25 minutes. Marie and Danny estimated that they can do the project alone in

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Question 1068093: Marie Just on and Danny are working on their group project. If they work together they can finish it in 25 minutes. Marie and Danny estimated that they can do the project alone in 2 1/2 hours and 1 1/2 hours respectively. If Jon will work alone, how long will it take him to finish the project?
Answer by ikleyn(52775) About Me  (Show Source):
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Marie, highlight%28cross%28Just%29%29 highlight%28cross%28on%29%29 John and Danny are working on their group project.
If they work together they can finish it in 25 minutes. Marie and Danny estimated that they can do the project alone in 2 1/2 hours
and 1 1/2 hours respectively. If Jon will work alone, how long will it take him to finish the project?
~~~~~~~~~~~~~~~~~~~~~~~ 

1.  2 1%2F2 hours = 150 minutes.

    1 1%2F2 hours =  90 minutes.


2.  If the three work together, their combined rate is 1%2F25 of the job per minute.

    In other words, if all three work together, they make 1%2F25 of the job per minute.


3.  If Marie and Danny work together, their combined rate is 1%2F150+%2B+1%2F90 = 3%2F450+%2B+5%2F450 = 8%2F450 of the job per minute.


4.  It implies that the John's individual rate of work is 

    1%2F25+-+8%2F450 = 18%2F450-8%2F450 = 10%2F450 = 1%2F45 of the job per minute.

    Hence, it will take 45 minutes for John to complete the job working alone.

Answer. It will take 45 minutes for John to complete the job working alone.

Solved.


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".