Question 606222
{{{ d = r*t }}}
On 1st trip,
{{{ r[1] = 40 }}} mi/hr
(1) {{{ d = 40t[1] }}}
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On 2nd trip,
{{{ r[2] = 24 }}} mi/hr
{{{ t[2] = t[1] + .5 }}}
(2) {{{ d = 24*( t[1] + .5 ) }}}
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By substitution:
{{{ 40t[1] = 24t[1] + 12 }}}
{{{ 16t[1] = 12 }}}
{{{ t[1] = .75 }}}
and, since
(1) {{{ d = 40t[1] }}}
(1) {{{ d = 40*.75 }}}
(1) {{{ d = 30 }}} 
The appointment is 30 mi away
check:
(2) {{{ d = 24*( t[1] + .5 ) }}}
(2) {{{ d = 24*( .75 + .5 ) }}}
(2) {{{ d = 24*1.25 }}
(2) {{{ d = 30 }}} 
OK