Question 1065649
Let {{{ d }}} = the distance in miles that the
one who drove for the shorter time traveled
{{{ 63 - d }}} = the distance in miles the one
who drove for the longer time traveled
Let {{{ t }}} = time in hrs that the one who
drove for the shorter time traveled
{{{ t + 12/60 }}}  = time in hrs that the one 
who drove for the longer time traveled
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(1) {{{ d = 45t }}}
(2) {{{ 63 - d = 45*( t + 1/5 ) }}}
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( note that {{{ 12/60 = 1/5 }}} )
(2) {{{ 63 - d = 45t + 9 }}}
(2) {{{ d + 45t = 54 }}}
Substitute (1) into (2)
(2) {{{ 45t + 45t = 54 }}}
(2) {{{ 90t = 54 }}}
(2) {{{ t = 3/5 }}} hrs
Convert to minutes
(2) {{{ t = ( 3/5 )*60 }}}
(2) {{{ t = 36 }}} min
and
{{{ 36 + 12 = 48 }}}
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One drove for 36 min
The other drove for 48 min
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check:
(1) {{{ d = 45t }}} ( {{{ t }}} must be in hrs here )
(1) {{{ d = 45*(3/5) }}}
(1) {{{ d = 27 }}} mi
and
(2) {{{ 63 - d = 45*( t + 1/5 ) }}}
(2) {{{ 63 - d = 45*( 3/5 + 1/5 ) }}}
(2) {{{ 63 - d = ( 4/5 )*45 }}}
(2) {{{ 63 - d = 36 }}}
(2) {{{ d = 63 - 36 }}}
(2) {{{ d = 27 }}} mi
OK