Question 1140373
{{{1/x+1/40=1/30}}}
{{{Solve}}}


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Read the description.  The filling rates for the pool represent or can represent fractions.  Numerator:  How many pools-worth of volume; Denominator:  How much time.   Amount of time for the smaller hose may be a variable x.   This variable x might or might not be a fraction.  Solve the equation and find out.


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One way is isolate the variable expression and solve just for it first.
LCD for {{{1/40}}} and {{{1/30}}}  is  120.


{{{1/x+1/40-1/40=1/30-1/40}}}

{{{1/x=(1/30)(4/4)-(1/40)(3/3)}}}

{{{1/x=4/120-3/120=1/120}}}

{{{1/x=1/120}}}
Obviously {{{highlight(x=120)}}}{{{minutes}}}