Question 536726
What are their rates of filling the trough?
Hose 1: ( 1 trough ) / ( 20 min )
Hose 2: ( 1 trough ) / ( 16 min )
How much of the trough does hose 2 get
filled in the 1st 4 minutes?
{{{ (1/16)*4 = 1/4 }}}
That means there is {{{ 3/4 }}} of the trough
left to be filled using both hoses
Let {{{t}}} = time to fill 3/4 of trough with both hoses 
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Add their rates of filling to get the rate 
with both filling
{{{ 1/20 + 1/16 = (3/4)/t }}}
{{{ 1/20 + 1/16 = 3/(4t)  }}}
Multiply both sides by {{{4}}}
{{{ 1/5 + 1/4 = 3/t }}}
Multiply both sides by {{{20t}}}
{{{ 4t + 5t = 60 }}}
{{{ 9t = 60 }}}
{{{ t = 6.667 }}} min
{{{ .667*60 = 40 }}} sec
The 1st hose will be used for 6 min and 40 sec
check answer:
{{{ 1/20 + 1/16 = (3/4)/t }}}
{{{ .05 + .0625 = .75/6.667 }}}
{{{ .1125 = .75/6.667 }}}
{{{ .7500375 = .75 }}} ( error is from rounding )
OK