this is in relation to intermediate algebra

Algebra
Tutor: None Selected Time limit: 1 Day

Leela and Zoe can weed the vegetable garden in 2 6/7 hours. Working alone it will take Leela 6 more hours

 to complete the work than it would take Zoe. How long would it take each of them to complete the gardening if they worked alone?

Jul 20th, 2015

Thank you for the opportunity to help you with your question!

leelas time when working alone take as t

zoes time when working alone take as b

when work together,

1/ total time =  1/ leelas time when working alone ( t)   +   1/ zoes time when working alone (b)

 1/  2 6/7  =   1/ leelas time when working alone  ( t) +   1/ zoes time when working alone(b)


and it is given that Leela 6 more hour  to complete the work than it would take Zoe.



please wait...i will submit the rest within 10 minutes...


Please let me know if you need any clarification. I'm always happy to answer your questions.
Jul 20th, 2015

I also know that  leela takes 6 hours longer than Bill, so t = b +6 .

 Then  1/b + 1/(b + 6) = 1/ 2 6/7

          1/b + 1/(b + 6) = 1/ 20/7

           1/b + 1/(b + 6) =  7 /20

         b + 6 + b  /  b ( b+ 6 ) = 7/20

         20 (   2b + 6 ) = (b ( b + 6) )7

        40 b + 120 = (b^2+6b)7

          40 b + 120 = 7 b^2+ 42 b

      7 b^2+ 2 b - 120 = 0

on solving,

 b= 4   or -30 /7 


b will not be negative,

so b= 4...


so b ( Zoe ) will take 4 hours to complete work alone.......................ANSWER


next is of leela ..it is so much to type...i will submit now ...please give 5 minutes


      

Jul 20th, 2015

leela takes 6 hours more than zoe

so leela takes = 6 + 4 = 10 hours


so ANSWER IS    leela takes 10 hours 

                              zoe takes  4 hours................


hope you understood...please message if you have any doubts...thank you

Jul 20th, 2015

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