Question 451900
Time for A and B:
(1) {{{ 13 + 19/23 }}} hrs
Time for B and C:
(2) {{{ 13 + 1/5 }}} hrs
Time for A and C:
(3) {{{ 17 + 5/23 }}} hrs
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(1) {{{ 13 + 19/23 }}}
(1) {{{ 299/23 + 19/23 }}}
(1) {{{ 318/23 }}}
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(2) {{{ 13 + 1/5 }}}
(2) {{{ 66/5 }}}
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(3) {{{ 17 + 5/23 }}}
(3) {{{ 391/23 + 5/23 }}}
(3) {{{ 396/23 }}}
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Let their rates of working =
{{{r[A]}}}, {{{r[B]}}}, and {{{r[C]}}}
given:
(1) {{{ r[A] + r[B] = 1 / (318/23) }}}
(2) {{{ r[B] + r[C] = 1 / (66/5) }}}
(3) {{{ r[A] + r[C] = 1 / (396/23) }}}
Note that the right sides mean ( 1 job) / ( time to do that job)
This is 3 equations and 3 unknowns, so it's solvable
Subtract (3) from (1)
(1) {{{ r[A] + r[B] = .072327 }}}
(3) {{{- r[A] - r[C] =- .058080 }}}
{{{ r[B] - r[C] = .014247 }}}
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Add this to (2)
(2) {{{ r[B] + r[C] = .075757 }}}
     {{{ r[B] - r[C] = .014247 }}}
{{{ 2r[B] = .090004 }}}
{{{ r[B] = .045002 }}}
{{{ r[B] = 1/22.22 }}}
and
(2) {{{ .045002 + r[C] = .075757 }}}
{{{ r[C] = .030755 }}}
{{{ r[C] = 1/32.52
and
(1) {{{ r[A] + .045002 = .072327 }}}
{{{ r[A] = .027325 }}}
{{{ r[A] = 36.60 }}}