SOLUTION: Two pipes together can fill a large tank in 10 hours. One of the pipes, used alone, takes 15 hours longer than the other to fill the tank. How long would each pipe take to fill the

Algebra ->  Test -> SOLUTION: Two pipes together can fill a large tank in 10 hours. One of the pipes, used alone, takes 15 hours longer than the other to fill the tank. How long would each pipe take to fill the      Log On


   



Question 820962: Two pipes together can fill a large tank in 10 hours. One of the pipes, used alone, takes 15 hours longer than the other to fill the tank. How long would each pipe take to fill the tank alone?
Answer by TimothyLamb(4379) About Me  (Show Source):
You can put this solution on YOUR website!
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x + y = V/10
x = V/T
y = V/(T + 15)
V/T + V/(T + 15) = V/10
1/T + 1/(T + 15) = 1/10
(T + 15)/T(T + 15) + T/T(T + 15) = 1/10
T + 15 + T = T(T + 15)/10
(1/10)TT + (15/10)T - 2T - 15 = 0
(1/10)TT + (15/10)T - (20/10)T - 15 = 0
(1/10)TT - (1/2)T - 15 = 0
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the above quadratic equation is in standard form, with a=0.1, b=-0.5, and c=-15
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to solve the quadratic equation, by using the quadratic formula, copy and paste this:
0.1 -0.5 -15
into this solver: https://sooeet.com/math/quadratic-equation-solver.php
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the two real roots (i.e. the two x-intercepts), of the quadratic are:
T = 15
T = -15
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negative time doesn't make sense, so use the positive root
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answer:
first pipe fills tank in 15 hours
second pipe fills tank in 30 hours
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Solve and graph linear equations:
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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:
https://sooeet.com/math/system-of-linear-equations-solver.php