SOLUTION: Jared, Kitt, and Laura deliver advertising flyers in Baltimore. Working alone, it takes Jared 14 hours to deliver all the flyers, and it takes Laura 3 hours longer than Kitt. Worki

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Question 786062: Jared, Kitt, and Laura deliver advertising flyers in Baltimore. Working alone, it takes Jared 14 hours to deliver all the flyers, and it takes Laura 3 hours longer than Kitt. Working together, they can deliver all the flyers in 40% of the time it takes Kitt working alone. How long does it take Kitt to do the delivery alone?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Jared, Kitt, and Laura deliver advertising flyers in Baltimore.
Working alone, it takes Jared 14 hours to deliver all the flyers, and it takes Laura 3 hours longer than Kitt.
Working together, they can deliver all the flyers in 40% of the time it takes Kitt working alone.
How long does it take Kitt to do the delivery alone?
:
Let k = time for Kitt working alone
then
(k+3) = time for Laura working alone
and
.4k = time required when working together
:
Let the completed job = 1, (all flyers delivered)
:
Each will do a fraction of the job, the 3 fractions add up to 1
%28.4k%29%2F14 + %28.4k%29%2Fk + %28.4k%29%2F%28%28k%2B3%29%29 = 1
in the middle fraction cancel k
%28.4k%29%2F14 + .4 + %28.4k%29%2F%28%28k%2B3%29%29 = 1
%28.4k%29%2F14 + %28.4k%29%2F%28%28k%2B3%29%29 = 1 - .4
%28.4k%29%2F14 + %28.4k%29%2F%28%28k%2B3%29%29 = .6
multiply by 14(k+3) to clear the fractions, resulting in:
.4k(k+3) + 14(.4k) = 14(k+3)*.6
.4k^2 + 1.2k + 5.6k = 8.4(k+3)
.4k^2 + 6.8k = 8.4k + 25.2
Combine on the left to form a quadratic equation
.4k^2 + 6.8k - 8.4k - 25.2 = 0
.4k^2 - 1.6k - 25.2 = 0
Simplify divide equation by .4, resulting in
k^2 - 4k - 63 = 0
This equation solved by the quadratic formula
I go a positive solution of 10.185 hrs for Kitt working alone
:
You can confirm this in the original shared work equation.