Question 894720
Each machine has a rate of printing expressed as:
( number of printing jobs finished ) / ( time to do all those jobs in hrs )
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Let {{{ R[a] }}} = A's rate of printing
Let {{{ R[b] }}} = B's rate of printing
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Note that {{{ 24 }}} min = {{{ 24/60 = .4 }}} hrs
and {{{ 36 }}} min = {{{ 36/60 = .6 }}} hrs
Given:
(1) {{{ R[a] + R[b] = 1 / 2.4 }}}
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In {{{ 36 }}} minutes, how much of the job did
the machines finish working together?
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In {{{ 2.4 }}} hrs, they would have done the whole job
They finished {{{ .6 / 2.4 = 1/4 }}} of the job in {{{ 36 }}} min
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There is {{{ 3/4 }}} of the job left to do
It took {{{ 3 }}} hrs for A to finish the job alone, so
A's rate of printing is:
{{{ R[a] = ( 3/4) / 3 }}}
{{{ R[a] = 1/4 }}} jobs / hr
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Now I can say:
(1) {{{ R[a] + R[b] = 1 / 2.4 }}}
(1) {{{ 1/4 + R[b] = 1 / 2.4 }}}
(1) {{{ 1/4 + R[b] = 10/24 }}}
(1) {{{ 6/24 + R[b] = 10/24 }}}
(1) {{{ R[b] = 4/24 }}}
(1) {{{ R[b] = 1/6 }}} jobs/hr
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A would take 4 hrs to do the job alone
B would take 6 hrs to do the job alone
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check:
(1) {{{ R[a] + R[b] = 1 / 2.4 }}}
(1) {{{ 1/4 + 1/6 = 1 / 2.4 }}}
(1) {{{ 6/24 + 4/24 = 10/24 }}}
(1) {{{ 10/24 = 10/24 }}}
OK