Question 857185
Let the rates that the 3 workmen work in
( jobs completed ) / ( days to complete them ) =
{{{ R[1] }}}, {{{ R[2] }}}, and {{{ R[3] }}}
given:
(1) {{{ R[2] + R[3] = 1/10 }}}
(2) {{{ R[1] + R[3] = 1/12 }}}
(3) {{{ R[1] + R[2] = 1/15 }}}
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Subtract (3) from (2)
(2) {{{ R[1] + R[3] = 1/12 }}}
(3) {{{ -R[1] - R[2] = -1/15 }}}
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{{{ R[3] - R[2] = 1/12 - 1/15 }}}
Add this result to (1)
{{{ -R[2] + R[3] = 1/12 - 1/15 }}}
(1) {{{ R[2] + R[3] = 1/10 }}}
{{{ 2*R[3] = 1/10 + 1/12 - 1/15 }}}
{{{ R[3] = 1/20 + 1/24 + 1/30 }}}
{{{ R[3] = 12/240 + 10/240 + 8/240 }}}
{{{ R[3] = 30/240 }}}
{{{ R[3] = 1/8 }}}
The 3rd, working alone can do
the job in 8 days
You can find {{{ R[1] }}} and {{{ R[2] }}}