SOLUTION: It takes Phoebe and Karen 2 hours and 40 minutes in making a long gown.working alone Karen would need 4 hours longer than Phoebe to finish the job.How long will each of them to do

Question 1132269: It takes Phoebe and Karen 2 hours and 40 minutes in making a long gown.working alone Karen would need 4 hours longer than Phoebe to finish the job.How long will each of them to do the job alone?

Found 2 solutions by ankor@dixie-net.com, MathTherapy:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
It takes Phoebe and Karen 2 hours and 40 minutes in making a long gown.
working alone Karen would need 4 hours longer than Phoebe to finish the job.
How long will each of them to do the job alone?
:
Change 2 hr 40 min to 2.667 hrs
:
let p = Phoebe's time working alone
Karen takes 4 hrs longer, therfore
(p+4) = time required by Karen alone
Let the complete job = 1
;
each will do a fraction of the job, the two fractions add up to 1.
+ = 1
multiply by p(p+4), cancel the denominators
2.667(p+4) + 2.667p = p(p+4)
2.667p + 10.667 + 2.667p = p^2 + 4p
5.33p + 10.67 = p^2 + 4p
arrange as a quadratic equation on the right
0 = p^2 + 4p - 5.33p - 10.67
p^2 - 1.33p - 10.67 = 0
Use the quadratic formula; a=1; b=-1.33; c=-10.67
the positive solution
p = 4.0 hrs. for Pheobe alone
and add 4:
8 hrs for Karen alone
;
:
Check using your calc
+ =

Answer by MathTherapy(10557) (Show Source): You can put this solution on YOUR website!

It takes Phoebe and Karen 2 hours and 40 minutes in making a long gown.working alone Karen would need 4 hours longer than Phoebe to finish the job.How long will each of them to do the job alone?

Let time Karen takes be H
Then time Phoebe takes = H - 4
And, Karen and Phoebe can do of job in 1 hour, respectively
We then get: ======> ======>
8(H - 4) + 8H = 3H(H - 4) -------- Multiplying by LCD, 3H(H - 4)

3H(H - 8) - 4(H - 8) = 0
(H - 8)(3H - 4) = 0_____H - 8 = 0 OR
H, or time Karen takes:
Time Phoebe takes:
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