URGENT! Need help with a 'work' problem.

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ReaPERudite

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Nov 2, 2019
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Cherry and Chanda are building a fence together. It takes Cherry 4 hours and Chanda 5 hours to build the fence alone. Cherry works on the fence for 1 hour before Chanda joins her. Unfortunately, Chanda brings RJ who can destroy the same fence in 3 hours. RJ tells Cherry and Chanda that he will stop destroying the fence when it is completely finished. How long do Cherry and Chanda work together, in hours, to finish building the fence?

The answer to the problem is apparently 45/7 hours. I tried the problem, and I keep getting 60/7 hours as the answer. Any ideas/answers?
 
ReaPERudite said:
Cherry and Chanda are building a fence together. It takes Cherry 4 hours and Chanda 5 hours to build the fence alone. Cherry works on the fence for 1 hour before Chanda joins her. Unfortunately, Chanda brings RJ who can destroy the same fence in 3 hours. RJ tells Cherry and Chanda that he will stop destroying the fence when it is completely finished. How long do Cherry and Chanda work together, in hours, to finish building the fence?

The answer to the problem is apparently 45/7 hours. I tried the problem, and I keep getting 60/7 hours as the answer. Any ideas/answers?
Click to expand...
Please post your work.
 
ReaPERudite said:
… Any ideas/answers?
Click to expand...
Hello ReaPERudite. My first suggestion is to read the forum's guidelines (i.e., Read Before Posting notice). We don't provide answers, in general, and we can't comment on your result without seeing what you did. Thanks!

?
 
What part of the job remains to be done when Chanda first arrives?
 
Hi ReaPERudite

The additional advice I'd offer, as a hint, is that it might be useful to convert the construction times in to rates, because these are directly additive. In other words, you have some values that are in "hours per fence", but it might be useful to have quantities in "fences per hour". Hint: mathematically, what is the only difference between RJ's rate and the other two?
 
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