superprismatic Posted September 17, 2009 Report Share Posted September 17, 2009 Here's a cute little problem I read in one of Martin Gardner's pieces a while back. When I first tried to work it, I made lots of equations and even more variables and, well, generally botched it! I am paraphrasing Gardners wording of it, so forgive my lack of eloquence. I searched on this site for it without success. If it was never on this site, it certainly deserves to be here! My wife drives me to and from work every day along the same route, both coming and going. I leave work at precisely the same time, 5 PM, that my wife pulls up in the car. One day, my boss let me leave early. I left work at exactly 4 PM. Rather than wait an hour for my wife to get there, I decided to walk along the route that she takes. At some point, she saw me walking, picked me up, did a U-turn, and drove home. I noticed that we arrived home 10 minutes earlier than we usually do. How long had I been walking before my wife picked me up? Assume idealized conditions, i.e., the car trip from home to work takes precisely the same time as from work to home, U-turns and getting into the car are instantaneous events, etc. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted September 17, 2009 Report Share Posted September 17, 2009 55 minutes. This is without any calculations, so if this is the right answer, I'll explain why! Quote Link to comment Share on other sites More sharing options...
0 superprismatic Posted September 17, 2009 Author Report Share Posted September 17, 2009 55 minutes. This is without any calculations, so if this is the right answer, I'll explain why! Yes! It's very simple when you look at it the right way, isn't it? Quote Link to comment Share on other sites More sharing options...
0 Guest Posted September 17, 2009 Report Share Posted September 17, 2009 The ten minutes that was saved was obtained from them meeting (her picking him up) earlier than normal. She was able to pick him up early because of the shorter distance she had to drive. This saved distance would be the same both directions and the time saved would be equally split, coming and going. The ten minutes saved resulted from a one way trip that was five minutes shorter. 5 PM minus 5 minutes = 4:55 PM He walked for 55 minutes. Quote Link to comment Share on other sites More sharing options...
0 superprismatic Posted September 17, 2009 Author Report Share Posted September 17, 2009 The ten minutes that was saved was obtained from them meeting (her picking him up) earlier than normal. She was able to pick him up early because of the shorter distance she had to drive. This saved distance would be the same both directions and the time saved would be equally split, coming and going. The ten minutes saved resulted from a one way trip that was five minutes shorter. 5 PM minus 5 minutes = 4:55 PM He walked for 55 minutes. Yep! Easy when you look at it correctly! Quote Link to comment Share on other sites More sharing options...
0 Guest Posted September 17, 2009 Report Share Posted September 17, 2009 solving graphically I found 55 minutes Quote Link to comment Share on other sites More sharing options...
0 superprismatic Posted September 17, 2009 Author Report Share Posted September 17, 2009 solving graphically I found 55 minutes Graphically? Quote Link to comment Share on other sites More sharing options...
0 Guest Posted September 17, 2009 Report Share Posted September 17, 2009 (edited) 5 min saved each way so wife picked him up at 4:55, walked for 55 mins Edited September 17, 2009 by Annette Quote Link to comment Share on other sites More sharing options...
0 superprismatic Posted September 17, 2009 Author Report Share Posted September 17, 2009 5 min saved each way so wife picked him up at 4:55, walked for 55 mins You got the trick of looking at the driver's point of view. Otherwise, things get messy. You've got it! Quote Link to comment Share on other sites More sharing options...
Question
superprismatic
Here's a cute little problem I
read in one of Martin Gardner's
pieces a while back. When I first
tried to work it, I made lots of
equations and even more variables
and, well, generally botched it!
I am paraphrasing Gardners wording
of it, so forgive my lack of
eloquence. I searched on this site
for it without success. If it was
never on this site, it certainly
deserves to be here!
My wife drives me to and from work
every day along the same route, both
coming and going. I leave work at
precisely the same time, 5 PM, that
my wife pulls up in the car. One
day, my boss let me leave early.
I left work at exactly 4 PM. Rather
than wait an hour for my wife to get
there, I decided to walk along the
route that she takes. At some point,
she saw me walking, picked me up,
did a U-turn, and drove home. I
noticed that we arrived home 10
minutes earlier than we usually do.
How long had I been walking before
my wife picked me up?
Assume idealized conditions, i.e.,
the car trip from home to work
takes precisely the same time as
from work to home, U-turns and
getting into the car are
instantaneous events, etc.
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