Question 781750
If {{{ R }}} = rate of working in ( jobs ) / ( hour ), then
(1) {{{ 8R[m] + 6R[w] + 12R[b] = 1 / (9*24) }}}
(2) {{{ 2*R[w] = 5*R[b] }}}
(3) {{{ 2*R[w] = 1*R[m] }}}
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This is 3 equations and 3 unknowns, so I can solve it
From (2) and (3),
{{{ R[m] = 5R[b] }}}
and, from (2),
{{{ R[w] = (5/2)*R[b] }}}
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Now, by substitution into (1),
(1) {{{ 8*R[m] + 6*R[w] + 12R[b] = 1 / (9*24) }}}
(1) {{{ 8*(5R[b]) + 6*((5/2)*R[b]) + 12R[b] = 1/216 }}}
(1) {{{ 40R[b] + 15R[b] + 12R[b] = 1/216 }}}
(1) {{{ ( 40 + 15 + 12 )*R[b] = 1/216 }}}
(1) {{{ 67R[b] = 1/216 }}}
(1) {{{ R[b] = 1/14472 }}}
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From (2)and (3),
{{{ R[m] = 5R[b] }}}
{{{ R[m] = 5/14472 }}}
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From (2),
{{{ R[w] = (5/2)*R[b] }}}
{{{ R[w] = 5/(2*14472) }}}
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Let {{{ h }}} = hours to do work
{{{ 12R[m] + 15R[w] + 10R[b] = 3/h }}}
{{{ 12*( 5/14472 ) + 15*( 5/( 2*14472 )) + 10*( 1/14472 ) = 3/h }}}
{{{ ( 1/14472 )*( 60 + 75/2 + 10 ) = 3/h  }}}
{{{ 177.5 / 14472 = 3/h }}}
{{{ h = ( 3*14472 ) / 177.5 }}}
{{{ h = 244.597 }}}
Number of 8 hr days is:
{{{ 244.597 / 8 = 30.575 }}}
30.575 8 hour days
check answer:
(1) {{{ R[b] = 1/14472 }}}
{{{ R[m] = 5/14472 }}}
{{{ R[w] = 5/(2*14472) }}}
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(1) {{{ 8R[m] + 6R[w] + 12R[b] = 1 / (9*24) }}}
(1) {{{ 8*(5/14472) + 6*(5/(2*14472)) + 12*(1/14472) = 1/216 }}}
(1) {{{ 40/14472 + 15/14472 + 12/14472 = 1/216 }}}
(1) {{{ 67/14472 = 1/216 }}}
(1) {{{ 67*216 = 14472 }}}
(1) {{{ 14472 = 14472 }}}
and
(2) {{{ 2*R[w] = 5*R[b] }}}
(2) {{{ 2*(5/( 2*14472 )) = 5*(1/14472) }}}
(2) {{{ 14472 = 14472 }}}
and
(3) {{{ 2*R[w] = 1*R[m] }}}
(3) {{{ 2*(5/(2*14472)) = 5*(1/14472) }}}
{{{ 14472 = 14472 }}}
OK
The method is good, I think, but I could easily 
made a mistake or 2