I need clarification and solution. James and Karen, helping together, can do a work for 2 hours. Working alone, James can do a work twice as long as Karen's? How many hours will it take for James to finish the work alone? How many hours will it take Karen to finish the work alone?
I need solution.



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We let Karen's time be x this would mean James' is 2x.
Then their rates is 1/x and 1/2x respectively:

1/[1/x+1/2x] = 2
1 = 2/x+1/x
1 = 3x/x²
x² = 3x
x²-3x = 0

x = 3 ± √9 = 3 ± 3 = 0 or 3
We cannot have 0 since their rates will be 1/0 which is undefined so we have x=3.

This means it will take James 6hours and Karen 3 hours to do it by themselves.
1 5 1
Got it, thanks:)
You're welcome!
youre so very genius
James will take 6 hours
Karen will take 3 hours