Question 1111965
Let {{{ t }}} = time in hrs for the larger pipe
to empty the pool
Rate of emptying for smaller pipe:
[ 1 pool emptied ] / [ 10 hrs ]
Rate of emptying for smaller pipe:
[ 1 pool emptied ] / [ t hrs ]
Add the rates of emptying to get the rate
with both pipes together
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{{{ 1/10 + 1/t = 1/3 }}}
{{{ 1/t = 10/30 - 3/30 }}}
{{{ 1/t = 7/30 }}}
Multiply both sides by {{{ 30t }}}
{{{ 30 = 7t }}}
{{{ t = 4.2857 }}} hrs
The larger pipe alone takes 4.2857 hrs
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check:
{{{ 1/10 + 1/4.2857 = 1/3 }}}
{{{ .1 + .2333 = .333 }}}
{{{ .333 = .333 }}}
OK