Question 831014
The rate for 4 men is 1 trench in 42 days
Let {{{ x }}} = the fraction of a trench dug
by 4 men in 1/2 day
{{{ 1/42 + x/((1/2)) }}}
{{{ 1/42 = 2x }}}
{{{ x = 1/84 }}}
----------------
That means there is {{{ 1 - 1/84 = 83/84 }}}
of a trench left to dig after 1/2 day
----------------
3 men have to finish the job
If 4 men take 42 days to dig a trench,
1 man takes 4 times as long, or {{{ 4*42 = 168 }}} days
3 men take 1/3 of that time, or 56 days
Let {{{y}}}  = the number of days for 3
men to dig {{{ 83/84 }}} of the trench
{{{ 1/56 = ( 83/84)/y }}}
{{{ y*( 1/56 ) = 83/84 }}}
{{{ y = ( 56*83) / 84 }}}
{{{ y = 4648/84 }}}
{{{ y = 55.333 }}}
It will take {{{ .5 + 55.333 = 55.5333 }}} days
to finish the job
----------------------
Hope I got it