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MATHS
Asked by Amy

# A swimming pool cam be filled by one hose in x days or by a different sized hose in y days. It can be filled using both hoses together in m days.Find a formula for m in terms of x and y, in its simplest form?

Let Volume of pool be V and flow rate of first hose be R1 For first hose we then get V=(R1)(x) Let flow rate of second hose be R2 For second hose we get equation V=(R2)(y) (same volume V to be filled) Using both hoses, the flow rate then become (R1+R2), with time m days So equation 3 is V=(R1+R2)m Substituting equation 1 and 2 into 3 for R1 and R2 we get V=((V/x)+(V/y))m Cancel out V (only possible because V not equal to 0) 1=((1/x)+(1/y))m So final answer gives relationship 1/m = 1/x + 1/y Hope that helps! ~Joe  Joseph Guillon
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