Question 1006200
The rate of filling with either the
fire hose or garden hose is expressed as:
[ fraction of pool filled ] / [ time to fill that fraction of pool ]
So, I will say:
{{{ r[1] }}} = rate of filling for garden hose
{{{ r[2] }}} = rate of filling for fire hose
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I can also say:
{{{ r[2] = 13.5r[1] }}}
also given:
{{{ r[1] + r[2] = 1/107 }}}
which is [ 1 pool filled ] / [ 107 minutes ]
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By substitution:
{{{ r[1] + 13.5r[1] = 1/107 }}}
{{{ 14.5r[1] = 1/107 }}}
{{{ r[1] = 1/1551.5 }}}
and
{{{ r[2] = 13.5r[1] }}}
{{{ r[2] = 13.5*( 1/1551.5 ) }}}
{{{ r[2] = 1/114.93 }}}
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For the garden hose:
{{{ 1551.5/60 = 25.858 }}}
{{{ .858*60 = 51.5 }}}
It will take 25 hrs 51.5 minutes
to fill the pool
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check:
{{{ r[1] + r[2] = 1/107 }}} 
{{{ 1/1551.5 + 1/114.93 = 1/107 }}}
{{{ .0006445 + .0087 = .009346 }}}
{{{ .0093445 = .009346 }}}
Looks close enough. These are pretty strange
numbers.  I would definitely get another
opinion on this. Hopefully, I got it