Question 955983
Let {{{ s }}} = the speed in mi/hr that he
has to drive to arrive on time at work
Let {{{ t }}} = time to get to work when
he arrives on time
Let {{{ d }}} = distance in miles to work
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Arriving 1 min early:
(1) {{{ d = 45*( t - 1/60 ) }}}
Arriving 1 min late:
(2) {{{ d = 40*( t + 1/60 ) }}}
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{{{ 45*( t-1/60 ) = 40*( t+1/60 ) }}}
{{{ 45t - 45/60 = 40t + 40/60 }}}
{{{ 5t = 85/60 }}}
{{{ t = 17/60 }}} hrs
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(2) {{{ d = 40*( t + 1 ) }}}
(2) {{{ d = 40*( 17/60 + 1 ) }}}
(2) {{{ d = 3080/60 }}} 
(2) {{{ d = 154/3 }}}
(2) {{{ d = 51.333 }}}
He lives 51.333 mi from work
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arriving 5 min early:
(1) {{{ d  = s*( 1 - 5/60 ) }}}
(1) {{{ 154/3 = s*( 55/60 ) }}}
(1) {{{ 154/3 = s*( 11/12 ) }}}
(1) {{{ 616/12 = s*( 11/12 ) }}}
(1) {{{ 11s = 616 }}}
(1) {{{ s = 56 }}}
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He has to drive 56 mi/hr to arrive 5 min early