Question 1134694
Add their rates of filling, which is:
[ how much of the tank is filled ] / [ time to fill that much ]
{{{ 1/1 }}} means 1 tank filled in 1 hr
Let {{{ t }}} = time in hrs to fill the tank with all 3 open
{{{ 1/60 + 1/25 + 1/15 = 1/t }}} ( in minutes )
{{{ 1/(60/60) + 1/(25/60) + 1/(15/60) = 1/t }}} ( in hrs )
{{{ 5/5 + 1/(5/12) + 1/(3/12) = 1/t }}}
{{{ 1 + 12/5 + 4 = 1/t }}}
Multiply both sides by {{{ 5t }}}
{{{ 5t + 12t + 20t = 5 }}}
{{{ 37t = 5 }}}
{{{ t = 5/37 }}} hrs
or
{{{ t = (5/37)*60 }}} min
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check:
{{{ 1 + 12/5 + 4 = 1/(5/37) }}}
{{{ 5 + 12/5 = 37/5 }}}
{{{ 25 + 12 = 37 }}}
OK