Question 972456
Add the rates of filling and subtract the
rate of draining for the 3 pipes to get
the rate of filling with all 3 open
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rates of filling:
[ 1 tank filled ] / [ 4 hrs ]
[ 1 tank filled ] / [ 6 hrs ]
rate of draining:
[ 1 tank drained ] / [ 3 hrs ]
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Let {{{ t }}} = time in hrs for the tank to be
filled with all 3 pipes open
{{{ 1/4 + 1/6 = 1/3 = 1/t }}}
Multiply both sides by {{{ 12t }}}
{{{ 3t + 2t - 4t = 12 }}}
{{{ t = 12 }}}
In 12 hrs, the tank will be filled with
all 3 pipes open
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check:
{{{ .25 + .1667 - .333 = .08333 }}}
{{{ .0834 = .0833 }}}
OK -error due to rounding off