Question 899706
Vince's head start is:
{{{ d[1] = 40*2 }}}
{{{ d[1] = 80 }}} km
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start a stopwatch when Sybil leaves
Let {{{ d }}} = distance Sybil travels 
until she overtakes Vince
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Let {{{ t }}} = time it takes for her to
catch Vince
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Vince's equation:
{{{ d - 80 = 40t }}}
Sybil's equation:
{{{ d = 50t }}}
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By substitution:
{{{ 50t - 80 = 40t }}}
{{{ 10t = 80 }}}
{{{ t = 8 }}}
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and
{{{ d = 50t }}}
{{{ d = 50*8 }}}
{{{ d = 400 }}}
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Sybil overtakes Vince 400 km down the road
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check:
{{{ d - 80 = 40t }}}
{{{ 400 - 80 = 40*8 }}}
{{{ 320 = 320 }}}
OK