SOLUTION: A new automatic machine can do a job in 1 hour less than an older machine. Together they can do the same job in 1.2 hours. How long would it take each machine to do the job alone?

Question 937584: A new automatic machine can do a job in 1 hour less than an older machine. Together they can do the same job in 1.2 hours. How long would it take each machine to do the job alone?
Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
x = time for old machine
y = time for new machine
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y = x - 1
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r = w/t
rates are additive:
r = 1/x + 1/y
t = w/r
t = 1/(1/x + 1/y)
1.2 = 1/(1/x + 1/y)
1.2(1/x + 1/y) = 1
1.2/x + 1.2/y = 1
1.2y/xy + 1.2x/xy = 1
1.2y + 1.2x = xy
1.2(y + x) = xy
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substitute y = x - 1
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1.2(x - 1 + x) = x(x - 1)
1.2(2x - 1) = xx - x
2.4x - 1.2 = xx - x
xx - x - 2.4x + 1.2 = 0
xx - 3.4x + 1.2 = 0
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the above quadratic equation is in standard form, with a=1, b=-3.4 and c=1.2
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to solve the quadratic equation, by using the quadratic formula, copy and paste this:
1 -3.4 1.2
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the quadratic has two real roots at:
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x = 3
x = 0.4
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the root x=0.4 makes y negative and doesn't fit the problem statement, so use the root x=3:
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x = 3
y = x - 1
y = 2
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answer:
x = time for old machine = 3 hours
x = time for new machine = 2 hours
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