SOLUTION: I need a bit of help on this one.... It usually takes Eva 3 hours longer to do the monthly payroll than it takes Cindy. They start working on it together at 9.00 AM and at 5.00

Question 59923This question is from textbook Elementry and Intermediate algebra
: I need a bit of help on this one....
It usually takes Eva 3 hours longer to do the monthly payroll than it takes Cindy. They start working on it together at 9.00 AM and at 5.00 PM they have 90% of it done. If Eva took s 2 hour lunch break while Cindy had none, then how much longer will it take for them to finish the payroll working together?This question is from textbook Elementry and Intermediate algebra

Found 2 solutions by stanbon, ankor@dixie-net.com:
Answer by stanbon(48558) (Show Source):
You can put this solution on YOUR website!
It usually takes Eva 3 hours longer to do the monthly payroll than it takes Cindy. They start working on it together at 9.00 AM and at 5.00 PM they have 90% of it done. If Eva took s 2 hour lunch break while Cindy had none, then how much longer will it take for them to finish the payroll working together?
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Cindy DATA:
Time = x hrs./job ; Rate = 1/x job/hr.
-------------
Eva DATA:
Time = x+3 hrs/job ; Rate = 1/(x+3) job/hr.
--------------
Together DATA:
Rate = 1/x + 1/(x+3) = (2x+3)/(x^2+3x) job/hr
EQUATION:
Cindy worked 8 hrs.
Eva worked 6 hours.
8*(cindy rate) + 6(eva rate)= 0.9 job
8/x + 6/(x+3) = 9/10
8(x+3)10 + 6x(10)=9x(x+3)
80x+240+60x = 9x^2+27x
9x^2-113x-240=0
x=[113+-sqrt(113^2-4*9*-240]/18
x=[113+-sqrt21409]/18
x=[113+146,3181]/18
x=14.41 hrs
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If x = 14.41 the "working together rate" is
(2x+3)/(x^2+3x) job/hr = (31.81)/(14.41^2+3(14.41))=31.81/250.88 job/hr
EQUATION:
Let z be the number of hours required to "finish the job"
(finish the job means do 0.1 of it).
So, (31.81/250.88) z = 0.1
z=0.788 hr
z=0.788(60)=47.32 minutes (time required for them to finish the job together)
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Cheers,
Stan H.

Answer by ankor@dixie-net.com(12701) (Show Source):
You can put this solution on YOUR website!
It usually takes Eva 3 hours longer to do the monthly payroll than it takes Cindy. They start working on it together at 9.00 AM and at 5.00 PM they have 90% of it done. If Eva took s 2 hour lunch break while Cindy had none, then how much longer will it take for them to finish the payroll working together?
:
Start with what we know:
:
Together:
Cindy worked from 9 til 5 w/o lunch so she worked 8 hrs to be 90% done
:
Eva took a 2 hr lunch break so she worked 6 hrs to be 90% done
:
Let the completed job = 1, then 90% of the job = .9
:
Let t = the amt of time required when Cindy works by herself
Then (t+3) = amt of time required when Eva works by herself
:
An equation to get it 90% done
:
= .9
:
GEt rid of the denominators, mult eq by t(t+3):
8(t+3) + 6t = .9(t(t+3)
:
8t + 24 + 6t = .9t^2 + 2.7t
:
0 = .9t^2 + 2.7t - 8t - 6t - 24
:
A quadratic equation, use the quadratic formula:
.9t^2 - 11.3t - 24 = 0
:
The positive solution: t ~ 14.4 hrs for Cindy to complete the job by herself
Then we know that it took 17.5 hr for Eva to do it by herself
:
They ask how much longer it will take to complete the job.
Let x = the additional time required for them to complete the job:
Let 1 = the completed job
:
= 1
:
The common denominator would be 14.4*17.4 = 250.56, mult equation by that:
:
17.4(8+x) + 14.4(6+x) = 250.56
:
139.2 + 17.4x + 86.4 + 14.4x = 250.56
:
17.4x + 14.4x = 250.56 - 139.2 - 86.4
:
31.8x = 24.96
:
x = 24.96/31.8
:
x = .785 hrs to complete the job, that's about 47 minutes
:
:
To check it, using the time to complete the job together:
=
.610 + .395 = 1.005 which is pretty close