SOLUTION: 49x^2+9=42x x^-2-9x^1+18=0 Winston works faster. Winston can mow his dad's lawn in 1 hour less than it takes his brother willie. If they take 2 hours to mow it when working t

Algebra ->  Equations -> SOLUTION: 49x^2+9=42x x^-2-9x^1+18=0 Winston works faster. Winston can mow his dad's lawn in 1 hour less than it takes his brother willie. If they take 2 hours to mow it when working t      Log On


   

Question 54073: 49x^2+9=42x
x^-2-9x^1+18=0
Winston works faster. Winston can mow his dad's lawn in 1 hour less than it takes his brother willie. If they take 2 hours to mow it when working together, then how long would it take Winston working alone?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
49x^2+9=42x
Rewrite as:
49x^2-42x+9=0
49x^2-21x-21x+9=0
7x(x-3)-3(7x-3)=0
(7x-3)(7x-3)=0
x=3/7 of multiplicity two
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x^-2-9x^1+18=0
(x-3)(x-6)-0
x=3 or x=6
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Winston works faster. Winston can mow his dad's lawn in 1 hour less than it takes his brother willie. If they take 2 hours to mow it when working together, then how long would it take Winston working alone?
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Winston DATA:
time to do job = x hrs/job ; rate = 1/x job/hr
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Willie's DATA:
time to do job =(x+1) hr/job ; rate = 1/(x+1) job/hr.
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Working together DATA:
time to do the job = 2 hrs/job ; rate = 1/2 job/hr.
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EQUATION:
rate + rate = rate together
1/x + 1/(x+1) = 1/2
Multiply thru by 2x(x+1) to get:
2(x+1) + 2x = x(x+1)
2x + 2 + 2x = x^2 + x
x^2-3x-2=0
Using the quadratic formula:
x=[3+-sqrt(9+8)]/2
x=[3+-sqrt(17)]/2
x= (3+sqrt(17)/2 Hrs for Winston to do the job alone.
That's about 3.56 hrs. or 3 hr. 33.6 minutes
Cheers,
Stan H.