SOLUTION: 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

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: 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      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 210858: 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?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
(Cindt's rate) + (Eva's rate) = Rate working together
actually they worked together for 6 of the 8 hours
and Cindy worked 2 hours alone
Let t= hours it takes Cindy to finish 1 payroll
t+%2B+3= hours for Eva to finish 1 payroll
Let p= fraction of payroll completed in 6 hours
with both working together
1%2Ft+%2B+1%2F%28t%2B3%29+=+p%2F6
And Cindy working alone for 2 hours:
1%2Ft+=+%28.9+-+p%29%2F2
.9+-+p+=+2%2Ft
-p+=+2%2Ft+-+.9
p+=+.9+-+2%2Ft
and
1%2Ft+%2B+1%2F%28t%2B3%29+=+.9%2F6+-+2%2F%286t%29
Multiply both sides by 6t%2A%28t%2B3%29
6%2A%28t%2B3%29+%2B+6t+=+.15%2A6t%2A%28t%2B3%29+-+2%2A%28t%2B3%29
8%2A%28t%2B3%29+%2B+6t+=+.15%2A6t%2A%28t%2B3%29
8t+%2B+24+%2B+6t+=+.15%2A6t%2A%28t%2B3%29
14t+=+.9t%5E2+%2B+2.7t+-+24
.9t%5E2+-+11.3t+-+24+=+0
9t%5E2+-+113t+-+240+=+0
Use quadratic equation
t+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a+=+9
b+=+-113
c+=+-240
t+=+%28-%28-113%29+%2B-+sqrt%28+%28-113%29%5E2-4%2A9%2A%28-240%29+%29%29%2F%282%2A9%29+
t+=+%28113+%2B-+sqrt%28+12769+%2B+8640+%29%29%2F18+
t+=+%28113+%2B-+sqrt%28+21409+%29%29%2F18+
t+=+%28113+%2B-+146.32%29%2F18+
t+=+14.4 hrs
They have 10% of the job left
1%2Ft+%2B+1%28t%2B3%29+=+.1%2FT
1%2F14.4+%2B+1%2F17.4+=+.1%2FT
.0694+%2B+.0575+=+.1%2FT
T+=+.1%2F.12687
T+=+.788hrs
It will take them about 47.3 min to finish the job
(Unless I goofed)