Question 789186
You need an equation for Alan and an equation for Dave
You want to know when they are {{{ 250 }}} mi apart
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First, you want to know how much of a head start Alan has
Let {{{ d[1] }}} = his head start
{{{ d[1] = 55*1 }}}
{{{ d[1] = 55 }}} mi
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Start a stopwatch when Dave leaves
Let {{{ t }}} = time on stopwatch when they are {{{ 250 }}} mi apart
Let {{{ d }}} = distance that Dave has traveled 
when they are {{{ 250 }}} mi apart
{{{ 250 - d }}} = Alan's distance from starting point when 
they are {{{ 250 }}} mi apart
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Alan's equation:
(1) {{{ 250 - d - 55 = 55t }}}
( note that I had to subtract his head start )
Dave's equation:
(2) {{{ d = 65t }}}
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Substitute (2) into (1)
(1) {{{ 250 - 65t - 55 = 55t }}}
(1) {{{ 120t = 195 }}}
(1) {{{ t = 1.625 }}} hrs
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{{{ .625*60 = 37.5 }}}
They can talk for 1 hr 37 min 30 sec
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check:
(2) {{{ d = 65t }}}
(2) {{{ d = 65*1.625 }}}
(2) {{{ d = 105.625 }}}
and
(1) {{{ 250 - d - 55 = 55t }}}
(1) {{{ 250 - d - 55 = 55*1.625 }}}
(1) {{{ 195 - d = 89.375 }}}
(1) {{{ d = 195 - 89.375 }}}
(1) {{{ d = 105.625 }}}
OK