Question 321922
The assumption is that Bob stops immediately as they pass each other and turns around using no time. 
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For constant speed or rate,
Rate*Time=Distance
{{{R*t=D}}}
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For Joe traveling at 50 mph and meeting Bob in 1/2 mile,
{{{50*t=1/2}}}
{{{t=1/100}}} hour
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Since Bob starts at zero speed, the distance equation is slightly different than for Joe who's traveling at constant speed. 
{{{a=(vf-vi)/t}}} where a=acceleration, vf=Bob's final speed, vi=Bob's initial speed, t=time.
and also, 
{{{D=(1/2)at^2}}}
{{{D=(1/2)((vf-vi)/t)*t^2}}}
{{{D=(1/2)(vf-vi)*t}}}
{{{1/2=(1/2)(vf-0)*(1/100)}}}
{{{vf=100}}} mph
Bob will be traveling at 100 mph when they meet.