SOLUTION: Bob is driving west bound and passes Joe driving eastbound at 50mph. How fast will Bob have to drive if he turns around and catches Joe 1/2 mile down the road from where they firs

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Question 321922: Bob is driving west bound and passes Joe driving eastbound at 50mph. How fast will Bob have to drive if he turns around and catches Joe 1/2 mile down the road from where they first passed each other?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
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%2At=D
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For Joe traveling at 50 mph and meeting Bob in 1/2 mile,
50%2At=1%2F2
t=1%2F100 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=%28vf-vi%29%2Ft where a=acceleration, vf=Bob's final speed, vi=Bob's initial speed, t=time.
and also,
D=%281%2F2%29at%5E2
D=%281%2F2%29%28%28vf-vi%29%2Ft%29%2At%5E2
D=%281%2F2%29%28vf-vi%29%2At
1%2F2=%281%2F2%29%28vf-0%29%2A%281%2F100%29
vf=100 mph
Bob will be traveling at 100 mph when they meet.