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Question 928544: Two pipes can fill a tank in 23 minutes if both are turned on. If only the smaller pipe is used, it would take 22 minutes longer for it to fill the tank than it would take the larger pipe alone. How long will it take for the smaller pipe to fill the tank? (Round your answer to the nearest tenth.)
Answer by TimothyLamb(4379)   (Show Source):
You can put this solution on YOUR website! x = rate big pipe
y = rate small pipe
r = w/t
t = time big pipe
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big pipe:
x = 1/t
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small pipe:
y = 1/(t + 22)
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together:
x + y = 1/23
1/t + 1/(t + 22) = 1/23
(t + 22)/t(t + 22) + t/t(t + 22) = 1/23
(t + 22) + t = (1/23)t(t + 22)
2t + 22 = (1/23)tt + (22/23)t
(1/23)tt + (22/23)t - 2t - 22 = 0
(1/23)tt + (22/23)t - (46/23)t - 22 = 0
(1/23)tt - (24/23)t - 22 = 0
0.0434782608696tt - 1.04347826087t - 22 = 0
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the above quadratic equation is in standard form, with a=1/23, b=-24/23 and c=-22
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to solve the quadratic equation, by using the quadratic formula, copy and paste this:
0.0434782608696 -1.04347826087 -22
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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t = 37.4950976
t = -13.4950976
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the negative root doesn't fit the problem statement, so use the positive root:
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answer:
time big pipe = 37.5 hours
time small pipe = 59.5 hours
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Solve quadratic equations, quadratic formula:
https://sooeet.com/math/quadratic-formula-solver.php
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Solve systems of linear equations up to 6-equations 6-variables:
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