Question 849367
1/10 as many people would take 10 times
longer to do the same job, so
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{{{ (1/10)*20 = 2 }}} people take {{{ 90*10 = 900 }}}
hours to do the same job
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The rate that the 20 people work is ( 1 job ) / ( 90hrs )
= {{{ 1/90 }}}
The rate that the 2 people work is ( 1 job ) / ( 900 hrs )
= {{{ 1/900 }}}
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Let ( 1 job ) / ( h hours ) = {{{ 1/h }}} = the rate that
18 people work
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I can then say:
{{{ 1/90 - 1/900 = 1/h }}}
Multiply both sides by {{{ 900h }}}
{{{ 10h - h = 900 }}}
{{{ 9h = 900 }}}
{{{ h = 100 }}}
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( 100 hrs ) / ( 10 days ) = 10 hrs / day
So, 18 people need to work 10 hrs a day to
finish the job in 10 days