My Math Forum Quadratic equation word problem!! Need help :(

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 September 10th, 2014, 06:52 PM #1 Newbie   Joined: Sep 2014 From: Singapore Posts: 1 Thanks: 0 Quadratic equation word problem!! Need help :( A swimming pool can be filled with water by pipes A and B. I) pipe a alone takes x hours to fill the swimming pool. Write down an expression in terms of x for the fraction of the swimming pool filled in 1 hour by pipe a alone. Ii) pipe b alone takes 1 hour longer than pipe a to fill the swimming pool. Write down an expression in terms of x for the fraction of the swimming pool filled in one hour by pipe b alone. The swimming pool can be filled with water by pipes a and b together in 26/3 hours. Write down an equation in x and show that it reduces to 3x^2-49x-26=0 Solve the equation above give your answers to 3sf
September 10th, 2014, 07:40 PM   #2
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Quote:
 Originally Posted by Hanagal15 A swimming pool can be filled with water by pipes A and B. I) pipe a alone takes x hours to fill the swimming pool. Write down an expression in terms of x for the fraction of the swimming pool filled in 1 hour by pipe a alone.
$\displaystyle \frac1x$

Quote:
 Originally Posted by Hanagal15 Ii) pipe b alone takes 1 hour longer than pipe a to fill the swimming pool. Write down an expression in terms of x for the fraction of the swimming pool filled in one hour by pipe b alone.
$\displaystyle \frac{1}{1 + x}$

Quote:
 Originally Posted by Hanagal15 The swimming pool can be filled with water by pipes a and b together in 26/3 hours. Write down an equation in x and show that it reduces to 3x^2-49x-26=0
We want

$\displaystyle \frac{26}{3} \cdot\left(\frac{1}{x}+\frac{1}{1+x}\right)=1$

so,

$\displaystyle \frac{1}{x}+\frac{1}{1+x}=\frac{3}{26}$

$\displaystyle \frac{1+x}{x(1+x)}+\frac{x}{x(1+x)}=\frac{3}{26}$

$\displaystyle \frac{2x+1}{x^2+x}=\frac{3}{26}$

$\displaystyle 26(2x+1)=3(x^2+x)$

$\displaystyle 3x^2-49x-26=0$

Taking the positive root,

$\displaystyle x=\frac{49+\sqrt{2713}}{6}\approx16.8\text{ hours.}$

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