SOLUTION: Jack, Kay, and Lynn deliver advertising flyers in a small town. If each person works alone, it takes Jack 2 hours to deliver all the flyers, and it takes Lynn 5 hours longer than K

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Jack, Kay, and Lynn deliver advertising flyers in a small town. If each person works alone, it takes Jack 2 hours to deliver all the flyers, and it takes Lynn 5 hours longer than K      Log On


   

Question 1184361: Jack, Kay, and Lynn deliver advertising flyers in a small town. If each person works alone, it takes Jack 2 hours to deliver all the flyers, and it takes Lynn 5 hours longer than Kay. Working together, they can deliver all the flyers in 60% of the time it takes Kay working alone. How long does it take Kay to deliver all the flyers alone?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Jack, Kay, and Lynn deliver advertising flyers in a small town.
If each person works alone, it takes Jack 2 hours to deliver all the flyers, and it takes Lynn 5 hours longer than Kay.
Working together, they can deliver all the flyers in 60% of the time it takes Kay working alone.
How long does it take Kay to deliver all the flyers alone?
:
let x = time required by K working alone
then
.6x = time required all working together
and
(x+5) = time required by Lynn alone
also
2 hrs = Jack's time alone
:
Let the completed job = 1
:
jack + Kay + Lynn = completed job
%28.6x%29%2F2 + %28.6x%29%2Fx + %28.6x%29%2F%28x%2B5%29 = 1
multiply by 2x(x+5)
.6x(x(x+5) + .6x(2(x+5) + .6x(2x) = 2x(x+5)
.6x^2(x+5) + 1.2x(x+5) + 1.2x^2 = 2x^2 + 10x
divide thru by x
.6x(x+5) + 1.2(x+5) + 1.2x = 2x + 10
.6x^2 + 3x + 1.2x + 6 + 1.2x - 2x = 10
.6x^2 + 3.4x = 10 - 6
A quadratic equation
.6x^2 + 3.4x - 4 =
:
Using the quadratic formula a=.6, b=3.4, b=-4
x=1 is the positive solution
Kay works 1 hr alone to complete the job