SOLUTION: 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 t

Algebra ->  Rate-of-work-word-problems -> SOLUTION: 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 t      Log On


   

Question 47626: 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!
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?
Willie DATA:
Time to do the job= x hrs./job ; Rate =1/x job/hr.
Winston DATA:
Time to do the job= x-1 hr/job ; Rate = 1/(x-1) job/hr.
Together DATA:
Time to do the job= 2 hr/job ; Rate = 1/2 job/hr.
EQUATION:
Willie Rate + Winston Rate = Together Rate
1/x + 1/(x-1) = 1/2
[x-1+x]/[x(x-1)] = 1/2
2(2x-1)=x^2-x
4x-2=x^2-x
x^2-5x+2=0
x=[5+sqrt(25-4(2)]/2 or x=[5-sqrt(17)]/2
x=4.56 hr. or x= 0.438 hr.
x-1 = 3.56 hr (Time Winston would take working alone.)
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Cheers,
Stan H.