Question 718048
Let {{{ r[1] }}} = the rate that the man works
Let {{{ r[2] }}} = the rate that the boy works
Add their rates to get rate working together
( 1 job ) / ( 8 days ) is rate working together, so
(1) {{{ r[1] + r[2] = 1/8 }}}
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Then you are given the case with 2 times the rate for a man
and 4 times the rate for a boy
(2) {{{ 2r[1] + 4r[2] = 1/3 }}}
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Multiply both sides of (1) by {{{ 2 }}}
and subtract (1) from (2)
(2) {{{ 2r[1] + 4r[2] = 1/3 }}}
(1) {{{ -2r[1] - 2r[2] = -2/8 }}}
{{{ 2r[2] = 1/3 - 1/4 }}}
{{{ 2r[2] = 4/12 - 3/12 }}}
{{{ 2r[2] = 1/12 }}}
{{{ r[2] = 1/24 }}}
and, since
(1) {{{ r[1] + r[2] = 1/8 }}}
(1) {{{ r[1] + 1/24 = 1/8 }}}
(1) {{{ r[1] + 1/24 = 3/24 }}}
(1) {{{ r[1] = 2/24 }}}
(1) {{{ r[1] = 1/12 }}}
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A man, working alone can do 1 job in 12 days
A boy, working alone, can do 1 job in 24 days
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check the answer:
(2) {{{ 2r[1] + 4r[2] = 1/3 }}}
(2) {{{ 2*(1/12) + 4*(1/24) = 1/3 }}}
(2) {{{ 1/6 + 1/6 = 1/3 }}}
(2) {{{ 1/6 + 1/6 = 2/6 }}}
OK