Question 965020
Working together, their rate is:
[ 1 fence ] / [ 1 hr ]
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Let {{{ t }}} = time in hrs for Sam
to paint fence
{{{ 3t }}} = time for Bill to paint fence
( 3 times slower )
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Add their rates of painting to get
their rate painting together
{{{ 1/t + 1/(3t) = 1/1 }}}
Multiply both sides by {{{ 3t }}}
{{{ 3 + 1 = 3t }}}
{{{ 3t = 4 }}}
{{{ t = 4/3 }}}
and
{{{ 3t = 3*(4/3) }}}
{{{ 3t = 4 }}}
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{{{ t = 4/3 }}}
{{{ t = 1 + 1/3 }}}
Convert {{{ 1/3 }}} hr to minutes
{{{ (1/3)*60 = 20 }}}
Sam takes 1 hr 20 min to paint fence
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check:
{{{ 1/t + 1/(3t) = 1/1 }}}
{{{ 1/(4/3) + 1/(3*(4/3)) = 1/1 }}} 
{{{ 3/4 + 1/4  = 1 }}}
{{{ 1 = 1 }}}
OK