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September 10th, 2014, 05:52 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^249x26=0 Solve the equation above give your answers to 3sf 
September 10th, 2014, 06:40 PM  #2  
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,932 Thanks: 1127 Math Focus: Elementary mathematics and beyond  Quote:
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$\displaystyle \frac{26}{3} \cdot\left(\frac{1}{x}+\frac{1}{1+x}\right)=1$ so, $\displaystyle \frac{1}{x}+\frac{1}{1+x}=\frac{3}{26}$ $\displaystyle \frac{1+x}{x(1+x)}+\frac{x}{x(1+x)}=\frac{3}{26}$ $\displaystyle \frac{2x+1}{x^2+x}=\frac{3}{26}$ $\displaystyle 26(2x+1)=3(x^2+x)$ $\displaystyle 3x^249x26=0$ Taking the positive root, $\displaystyle x=\frac{49+\sqrt{2713}}{6}\approx16.8\text{ hours.}$  

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