Question 995963
Add their rates of filling to get rate filling together
A's rate:
[ 1 tank filled ] / [ 15 hrs ]
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Let {{{ t }}} = time in hrs for pipe B to fill tank alone
B's rate:
[ 1 tank filled ] / [ t hrs ]
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Their rate working to gether:
[ 1 tank filled ] / [ 6 hrs ]
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{{{ 1/15 + 1/t = 1/6 }}}
Multiply both sides by {{{ 30t }}}
{{{ 2t + 30 = 5t }}}
{{{ 3t = 30 }}}
{{{ t = 10 }}}
B alone can fill the tank in 10 hrs
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check:
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{{{ 1/15 + 1/t = 1/6 }}}
{{{ 1/15 + 1/10 = 1/6 }}}
{{{ 2/30 + 3/30 = 5/30 }}}
{{{ 5/30 = 5/30 }}}
OK