Question 723288
Let {{{ R }}} = the rate at which a single worker works
Add their rates of working to get their rate
working together
{{{ 30R = 1/60 }}}
( the {{{ 1/60 }}} means 1 wall / 60 days )
{{{ R = 1/1800 }}}
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The 30 workers work for 10 days.
Let {{{ x }}} = the fraction of the wall they finish
{{{ 30R = x/10 }}}
{{{ 1/60 = x/10 }}}
{{{ x = 1/6 }}}
So, 5/6 of the wall must be finished in {{{ 40 - 10 = 30 }}} days
Let {{{ n }}} = the number of additional workers needed  to
finish the wall in 30 more days
{{{ ( 30 + n )*R = ( 5/6 ) / 30 }}}
{{{ 30R + n*R = 5/180 }}}
{{{ n*R = 5/180 - 1/60 }}}
and, since {{{ R = 1/1800 }}}
{{{ n*( 1/1800 ) = 50 / 1800 - 30/1800 }}}
Multiply both sides by {{{ 1800 }}}
{{{ n = 20 }}}
20 workers must be added to finish in 40 days
check:
can {{{ 30 + 20 = 50 }}} workers do 5/6 of the wall
in 30 days?
{{{ 50R = ( 5/6 ) / 30 }}}
{{{ 50*180*R = 5 }}}
{{{ R = 5 / 9000 }}}
{{{ R = 1/1800 }}}
OK