Question 1020437
Add rates of filling and subtract rates
of draining
Rate for 1st inlet pipe:
[ 1 pool filled ] / [ 3 hrs ]
Rate for 2nd inlet pipe:
[ 1 pool filled ] / [ 5 hrs ]
Rate for outlet pipe:
[ 1 pool drained ] / [ 6 hrs ] ( subtract this rate )
Rate for all 3 pipes open:
[ fraction of the pool filled ] / [ 2 hrs ]
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I can write the equation:
{{{ 1/3 + 1/5 - 1/6 = x/2 }}}
Multiply both sides by {{{ 30 }}}
{{{ 10 + 6 - 5 = 15x }}}
{{{ 15x = 11 }}}
{{{ x = 11/15 }}}
11/15 of the pool got filled in 2 hrs
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Note that in 3 hrs, the pool is overflowing, since
{{{ 1/3 + 1/5 - 1/6 = x/3 }}}
{{{ 10 + 6 - 5 = 10x }}}
{{{ x = 11/10 }}}
( overflowed by {{{ 1/10 }}} )