SOLUTION: a Chinese restaurant has a large goldfish pond. Suppose that an inlet pipe and a hose together can fill the pond in 10 hours. The inlet pipe alone can complete the job in one hour

Question 927177: a Chinese restaurant has a large goldfish pond. Suppose that an inlet pipe and a hose together can fill the pond in 10 hours. The inlet pipe alone can complete the job in one hour less time than the hose alone. Find the time that the hose can complete the job alone and the time that the inlet pipe can complete the job alone.
Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
x = rate of inlet pipe
y = rate of hose
z = time of hose alone
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r = w/t
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x = 1/(z - 1)
y = 1/z
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x + y = 1/10
1/(z - 1) + 1/z = 1/10
10/(z - 1) + 10/z = 1
10z/z(z - 1) + 10(z - 1)/z(z - 1) = 1
10z + 10(z - 1) = z(z - 1)
10z + 10z - 10 = zz - z
zz - 21z + 10 = 0
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the above quadratic equation is in standard form, with a=1, b=-21 and c=10
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to solve the quadratic equation, by using the quadratic formula, copy and paste this:
1 -21 10
into this solver: https://sooeet.com/math/quadratic-equation-solver.php
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the quadratic has two real roots at:
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z = 20.5124922
z = 0.487507803
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use the root z = 20.5124922
the root z = 0.487507803 doesn't fit the problem statement, because we know that the pipe and hose together fill the pool in 10 hours, so the hose alone cannot possibly fill the pool in 0.49 hours:
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answer:
time of hose alone = 20.5 hours
time of pipe alone = 19.5 hours
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