SOLUTION: My question is: 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 d

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: My question is: 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 d      Log On


   

Question 194429: My question is: 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 ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
My question is: 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?
:
Let t = C's time working alone
then
(t+3) = E's time working alone
:
Let the completed job = 1
:
Working time to complete 90%: 9 Am to 5 Pm = 8 hrs
:
A shared work equation to complete 90% of the job:
8%2Ft + 8%2F%28%28t%2B3%29%29 = .9(1)
Multiply equation by t(t+3), results:
8(t+3) + 8t = .9t(t+3)
8t + 24 + 8t = .9t^2 + 2.7t
16t + 24 = .9t^2 + 2.7t
arrange as a quadratic equation
.9t^2 + 2.7t - 16t - 24 = 0
.9t^2 -13.3t - 24 = 0
Using the quadratic formula a-.9; b=-13.3; c=-24
The positive solution ~ 16.4 hrs is C's time alone
then; 19.4 hrs = E's time alone
:
then it says,"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?"
:
Let x = how much longer it will take to complete the job
Then
x+8 = C,s time on the job
and
x+6 = E's time because of a 2 hr lunch break
;
%28x%2B8%29%2F16.4 + %28x%2B6%29%2F19.4 = 1
Multiply equation by (16.4*19.4), results
19.4(x+8) + 16.4(x+6) = 16.4 * 19.4
:
19.4x + 155.2 + 16.4x + 98.4 = 318.16
:
35.8x + 253.6 = 318.16
:
35.8x = 318.16 - 253.6
x = 64.56%2F35.8
x = 1.8 hrs to finish the job