SOLUTION: Im not sure if i am getting this equation properly lined up. the question is it takes shawn 12 more hours to paint a house than Michelle. together it takes them 14.4 hours to com
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Question 725505: Im not sure if i am getting this equation properly lined up. the question is it takes shawn 12 more hours to paint a house than Michelle. together it takes them 14.4 hours to complete the work. how long would it take shawn to paint the house by himself?
Found 2 solutions by mananth, stanbon:
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
Michelle take x hours for 1 job
Michelle does 1/x of the job in 1 hour
Shawn takes x+12 hours
Shawn does 1/(x+12) of the job in 1 hour
together they complete of the job in 1 hour
They take 14.4 hours to do the job together
they do 1/14.4 of the job in 1 hour
multiply by 72x(x+12)
72(x+12)+72x=5x(x+12)
72x+864+72x=5x^2+60x
5x^2-84x-864=0
Find the roots of the equation by quadratic formula
a= 5 , b= -84 , c= -864
b^2-4ac= 7056 + 17280
b^2-4ac= 24336
x1=( 84 + 156 )/ 10
x1= 24.00
x2=( 84 -156 ) / 10
x2= -7.20
Ignore negative value
x= 24
Now you know how many hours Shawn will take
m.ananth@hotmail.ca
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
it takes shawn 12 more hours to paint a house than Michelle. together it takes them 14.4 hours to complete the work. how long would it take shawn to paint the house by himself?
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Shawn's rate = 1/(12+x) job/hr
Together rate = 1/14.4 job/hr
Michelle rate = 1/x job/hr
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Equation:
rate + rate = together rate
1/(12+x) + 1/x = 1/14.4
-------
[(x+12+x)]/[12x+x^2] = 1/14.4
----
[2x+12)/(x^2+12x) = 1/14.4
----
14.4(2x+12) = x^2+12x
28.8x + 172.8 = x^2+12x
x^2 -16.8x -172.8 = 0
x = 24 hrs (time for Michelle to do the job alone)
x+12 = 36 hs (time for Shawn to do the job alone)
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Cheers,
Stan H.
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