Question 770904
Let {{{ t }}} = the time in hours which 
would make her arrive on time
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{{{ t +  10/60  }}} = her time in hrs when
she drives {{{ 40 }}} mi/hr
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{{{ t -  10/60  }}} = her time in hrs when
she drives {{{ 60 }}} mi/hr 
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Let {{{ d }}} =distance in miles from home to school
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Equation for driving {{{ 40 }}} mi/hr:
(1) {{{ d = 40*( t + 10/60  ) }}}
Equation for driving {{{ 60 }}} mi/hr:
(2) {{{ d = 60*( t - 10/60  ) }}}
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(1) {{{ d = 40*( t + 1/6  ) }}}
(1) {{{ d = 40t + 20/3 }}}
and
(2) {{{ d = 60*( t - 1/6  ) }}}
(2) {{{ d = 60t - 10 }}}
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By substitution:
(2) {{{ 40t + 20/3 = 60t - 10 }}}
(2) {{{ 20t = 20/3 + 10 }}
(2) {{{ 20t = 20/3 + 30/3 }}}
(2) {{{ 20t = 50/3 }}}
(2) {{{ t = 5/6 }}}
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Plug this result back into either equation:
(2) {{{ d = 60*( 5/6 - 1/6  ) }}}
(2) {{{ d = 60*( 2/3 ) }}}
(2) {{{ d = 40 }}}
The distance in miles from home to school is 40 mi
check:
(1) {{{ d = 40*( t + 1/6  ) }}}
(1) {{{ 40 = 40*( t + 1/6  ) }}}
(1) {{{ 40 = 40*( 5/6 + 1/6  ) }}}
(1) {{{ 40 = 40*1 }}}
OK