A small pipe fills a water tank in $x$ minutes, whereas a larger pipe fills the same tank in \((x-

Question

A small pipe fills a water tank in $x$ minutes, whereas a larger pipe fills the same tank in $(x-8)\mathrm{ }$ minutes. Write down an expression, in terms of $x$, for the fraction of the tank filled with water in one minute using the small pipe, the large pipe. If both pipes are used together, then the tank can be filled in $7.5$ minutes. Form an equation involving $x$ and show that it reduces to ${{x}^{2}}-23x+60=0$. Solve the equation ${{x}^{2}}-23x+60=0$, giving your answers correct to $2$ decimal places. Hence, find the time taken to fill the tank using only the large pipe.

Accepted Answer

(a)(i) 1/x; (a)(ii) 1/(x-8); (c) x = 20.00 or 3.00; (d) 12 minutes.

Pipes and Time: Forming and Solving a Quadratic Equation

Pipes and Time: Forming and Solving a Quadratic Equation

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