Question 1012481
How much was Mark's head start?
Let {{{ r }}} = Marks rate in km/hr
Let {{{ d }}} = Mark's head start in km
{{{ t = 1/2 }}} hr
{{{ d[1] = r*t }}}
{{{ d[1] = r*(1/2) }}}
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Start a stopwatch when Carole leaves Cleveland
Let {{{ d }}} = distance Carole travels until they meet
{{{ r - 2 }}} = Carole's rate in km/hr
From 3:30 to 4:30 is {{{ 1 }}} hr, so
Carole's equation is:
{{{ d = ( r - 2 )*1 }}}
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Mark's equation:
{{{ 208 - r*(1/2) - ( r - 2 )*1 = r*1 }}}
{{{ 208 - r/2 - r + 2 = r }}}
{{{ r + r + r/2 = 210 }}}
{{{ (5/2)*r = 210 }}}
{{{ r = (2/5)*210 }}}
{{{ r = 84 }}} km/hr
and
{{{ r - 2 = 82 }}} km/hr
Mark's rate was 84 km/hr
Carole's rate was 82 km/hr
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check:
Carole's distance:
{{{ d = ( r - 2 )*1 }}}
{{{ d = 82 }}} km
Mark must have traveled {{{ 208 - 82 = 126 }}} km
in {{{ 3/2 }}} hrs at {{{ 84 }}} km/hr
{{{ 126 = 84*(3/2) }}}
{{{ 126 = 126 }}}
OK