```Question 596105
This says that 10 men could have done the job
in 40 days.
1 man would have taken 10 times as long, so
1 man does the job in 400 days
Let {{{ n }}} = number of days after start when 4 men leave job
{{{ 50 - n }}} = number of days after 4 men leave
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In general, ( rate of working for 1 man ) x ( number of men ) x ( number of days ) = part of job completed
( 1 job / 400 days ) x ( 10 men ) x ( n days ) = part of job completed
( 1 job / 400 days ) x ( 6 men ) x ( 50 - n days ) = part of job completed
The 2 parts add up to 1 job completed
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{{{ ( 1/400 )*10n + ( 1/400 )*6*( 50 - n ) = 1 }}}
{{{ ( 1/400 )*( 10n + 300 - 6n ) = 1 }}}
{{{ 4n + 300 = 400 }}}
{{{ 4n = 100 }}}
{{{ n = 25 }}}
{{{ 50 - n = 50 - 25 }}}
{{{ 50 - n = 25 }}}
The 4 men left 25 days after the work started
check:
{{{ ( 1/400 )*10n + ( 1/400 )*6*( 50 - n ) = 1 }}}
{{{ ( 1/400 )*10*25 + ( 1/400 )*6*( 50 - 25 ) = 1 }}}
{{{ 250/400 + ( 6*25 ) / 400 = 1 }}}
{{{ 250 + 150 = 400 }}}
{{{ 400 = 400 }}}
OK```