SOLUTION: If Ana can work twice as much as Eddie, and jhohn can finish the job less than an hour that of Ana. And Eddie can do it alone in 3 hours. How long would it take for the three of th

Algebra ->  Rate-of-work-word-problems -> SOLUTION: If Ana can work twice as much as Eddie, and jhohn can finish the job less than an hour that of Ana. And Eddie can do it alone in 3 hours. How long would it take for the three of th      Log On


   

Question 1068673: If Ana can work twice as much as Eddie, and jhohn can finish the job less than an hour that of Ana. And Eddie can do it alone in 3 hours. How long would it take for the three of them working together to finish the entire job.
Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
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If Ana can work twice as highlight%28cross%28much%29%29 fast as Eddie, and highlight%28cross%28jhohn%29%29 John can finish the job highlight%28cross%28less_than%29%29 in one hour sooner that of Ana.
And Eddie can do it alone in 3 hours. How long would it take for the three of them working together to finish the entire job.
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The condition says that Eddie can make a job in 3 hours.
Hence, Ana can do it in 1.5 hours.
Hence, John can finis the job in 1.5-1 = 0.5 hour.

Now, their rates of work are 1%2F3 of the job per hour (Eddie), 1%2F1.5 (Ana) and 1%2F0.5 (John).

Hence, their combined rate of work is the sum

1%2F3+%2B+1%2F1.5+%2B+1%2F0.5 = 1%2F3+%2B+2%2F3+%2B+6%2F3 = %281+%2B+2+%2B+6%29%2F3 = 9%2F3 = 3 jobs per hour.

Hence, they need 1%2F3 of an hour, or 20 minutes, to complete the job working together.

Solved.

For a wide variety of similar solved joint-work problems with detailed explanations 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
in this site.

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".