SOLUTION: together it takes dawn and deb 2 hr 55 min to sort recyclables. alone dawn would require 2 more hours then deb how long would it take deb to do the the job alone
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Question 1120492: together it takes dawn and deb 2 hr 55 min to sort recyclables. alone dawn would require 2 more hours then deb how long would it take deb to do the 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! together it takes dawn and deb 2 hr 55 min to sort recyclables.
alone dawn would require 2 more hours then deb
how long would it take deb to do the the job alone:
:
Change times to minutes
:
let d = time required by Dawn alone
then
(d-120) = time required by Deb
:
Change 2 hrs 55 min: to 175 min
:
Let the completed job = 1, each will do a fraction of the job, the fractions add up to 1 + = 1
multiply equation by d(d-120), cancel the denominators
175(d-120) + 175d = d(d-12)
175d - 21000 + 175d = d^2 - 120d
350d - 21000 = d^2 - 120d
form a quadratic equation on the right
0 = d^2 - 120d - 350d + 21000
d^2 - 470d + 21000 = 0
Solve with the quadratic formula a=1; b=-470; c=21000
Two solutions
d=50
d=420 min, the only one that makes sense
420/60 = 7 hrs Dawn working alone
then
7 - 2 = 5 hrs Deb working alone
You can put this solution on YOUR website! together it takes dawn and deb 2 hr 55 min to sort recyclables. alone dawn would require 2 more hours then deb how long would it take deb to do the the job alone
Let time Deb takes be D
Then time Dawn takes = D + 2
We then get:
35(D + 2) + 35D = 12D(D + 2) ------ Multiplying by LCD, 35D(D + 2)
6D(D - 5) + 7(D - 5) = 0
(D - 5)(6D + 7) = 0
Time Deb takes, or OR
