<PRE><B>Question 437909</B>
1 child would take 10 days to do a job
1 adult would take 6 days to do a job
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Building the tower, let {{{R[c]}}} = the rate that
children work.
Let {{{R[a]}}} = the rate that an adult works
44 adults in 5 days to build a tower
is {{{ 1/220}}} adults/day to build a tower
{{{ R[a]/R[c] = 10/6 }}}
{{{ R[a]/R[c] = (1/220) / R[c] }}}
{{{ 10/6 = (1/220) / R[c] }}}
{{{ R[c] = (6/10)*(1/220) }}}
{{{ R[c] = 3/1100 }}}
The rate for 40 adults is {{{ 40*R[a] = 40/220 }}}
The rate for 80 children is {{{ 80*R[c] = 240/1100 }}}
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Add the rates to get their rate working together
{{{ 40/220 + 240/1100 = 1/d }}}  (1 tower in d days)
{{{ 2/11 + 12/55 = 1/d }}}
Multiply both sides by {{{55d}}}
{{{ 10d + 12d = 55 }}}
{{{ 22d = 55 }}}
{{{ 2d = 5 }}}
{{{ d = 2.5 }}}
It will take 50 adults and 80 children 2.5 days to build a tower
  
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