Question 1032090
Add their rates of filling
Rate for 1st hose:
[ 1 tank filled ] / [ 1.5 hrs ]
Rate for 2nd hose:
[ 1 tank filled ] / [ .75 hrs ]
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Let {{{ t }}} = time in hrs to fill
the tank with both hoses
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{{{ 1/1.5 + 1/.75 = 1/t }}}
Multiply both sides by {{{ 1/4 }}}
{{{ 1/6 + 1/3  = 1/(4t) }}}
Multiply both sides by {{{ 12t }}}
{{{ 2t + 4t = 3 }}}
{{{ 6t = 3 }}}
{{{ t = 1/2 }}}
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It will take 1/2 hr to fill tank
with both hoses
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check:
{{{ 1/1.5 + 1/.75 = 1/t }}}
{{{ 1/1.5 + 1/.75 = 1/.5 }}}
{{{ 2/3 + 4/3 = 2 }}}
{{{ 6/3 = 2 }}}
{{{ 2 = 2 }}}
OK