Question 745794
You can add their rates of digging to get their rate 
working together
Let {{{ R[1] }}} = father's rate of digging
Let {{{ R[2] }}} = Son's rate of digging
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In general, I can say that:
( time spent digging ) x ( rate of digging ) = fraction of job done
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given:
(1) {{{ 6R[1] + 12R[2] = 1 }}}
(2) {{{ 9R[1] + 8R[2] = 1 }}}
( note that {{{ 1 }}} means entire job done )
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Multiply both sides of (1) by {{{ 3 }}} and
both sides of (2) by {{{ 2 }}}
Then subtract (2) from (1)
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(1) {{{ 18R[1] + 36R[2] = 3 }}}
(2) {{{ -18R[1] - 16R[2] = -2  }}}
{{{ 20R[2] = 1 }}}
{{{ R[2] = 1/20 }}}
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(1) {{{ 6R[1] + 12R[2] = 1 }}}
(1) {{{ R[1] + 2R[2] = 1/6 }}}
(1) {{{ R[1] + 2R[2] = 1/6 }}}
(1) {{{ R[1] + 2*(1/20) = 1/6 }}}
(1) {{{ R[1] = 1/6 - 1/10 }}}
(1) {{{ R[1] = 5/30 - 3/30 }}}
(1) {{{ R[1] = 2/30 }}}
(1) {{{ R[1] = 1/15 }}}
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The son would take 20 hrs working alone
check:
(2) {{{ 9R[1] + 8R[2] = 1 }}}
(2) {{{ 9*(1/15) + 8*(1/20) = 1 }}}
(2) {{{ 9/15 + 8/20 = 1 }}}
(2) {{{ 36/60 + 24/60 = 60/60 }}}
(2) {{{ 1 = 1 }}}
OK