Question 765329
Let Greg's rate of working = {{{ r[g] }}}
Let Nico's rate of working = {{{ r[n] }}}
Let Kiefer's rate of working = {{{ r[k] }}}
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(1) {{{ r[g] + r[n] = 1 /((3/8)) }}}
(2) {{{ r[g] + r[k] = 1 / ((3/7)) }}}
(3) {{{ r[g] + r[n] + r[k] = 1 / ((1/4)) }}}
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(1) {{{ r[g] + r[n] = 8/3 }}}
(2) {{{ r[g] + r[k] = 7/3 }}}
(3) {{{ r[g] + r[n] + r[k] = 12/3 }}}
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Substitute (1) into (3)
(3) {{{ 8/3 + r[k] = 12/3 }}}
(3) {{{ r[k] = 4/3 }}}
and
(2) {{{ r[g] + 4/3 = 7/3 }}}
(2) {{{ r[g] = 1 }}}
and
(1) {{{ 3/3 + r[n] = 8/3 }}}
(1) {{{ r[n] = 5/3 }}}
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(2) {{{ r[g] = 1 }}}
(2) {{{ r[g] = 1/1 }}}
and
(1) {{{ r[n] = 1 / 3/5 }}}
and
(3) {{{ r[k] = 1 / 3/4 }}}
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Greg takes 1 hr to complete puzzle
Nico takes 36 minutes to complete puzzle ( {{{ (3/5)*60 = 36 }}} )
Keifer takes 45 minutes to complete puzzle