Question 1088380
Let {{{ R[1] }}} = the rate that men work 
Let {{{ R[2] }}} = the rate that women work
( The rates are in [ work completed ] / [ days to complete the work ] )
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(1) {{{ 3R[1] + 7R[2] = 1/10 }}}
(2) {{{ 4R[1] + 6R[2] = 1/8 }}}
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Multiply both sides of (1) by {{{ 4 }}} and
both sides of (2) by {{{ 3 }}}
Then subtract (2) from (1)
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(1) {{{ 12R[1] + 28R[2] = 2/5 }}}
(2) {{{ -12R[1] - 18R[2] = -3/8 }}}
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(1) {{{ 12R[1] + 28R[2] = 16/40 }}}
(2) {{{ -12R[1] - 18R[2] = -15/40 }}}
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{{{ 10R[2] = 1/40 }}}
Ten women take 40 days to complete the work
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{{{ R[2] = 1/400 }}}
check answer:
(1) {{{ 3R[1] + 7R[2] = 1/10 }}}
(1) {{{ 3R[1] + 7*(1/400) = 1/10 }}}
(1) {{{ 1200R[1] + 7 = 40 }}}
(1) {{{ 1200R[1] = 33 }}}
(1) {{{ R[1] = 33/1200 }}}
(1) {{{ R[1] = 11/400 }}}
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(2) {{{ 4R[1] + 6R[2] = 1/8 }}}
(2) {{{ 4R[1] + 6*(1/400) = 1/8 }}} 
(2) {{{ 1600R[1] + 6 = 50 }}}
(2) {{{ 1600R[1] = 44 }}}
(2) {{{ R[1] = 44/1600 }}}
(2) {{{ R[1] = 11/400 }}}
OK
Check the math & get a 2nd opinion if needed