Time for MATH MINUTE! (provide your favorite theme music
here).
Get out
your paper & pencil, because I have a new puzzle for you!!
Hints/Responses: PUZZLE #88 Where to build the bridge?
A. There
are two towns on opposite sides of a river, Uptown and Downtown. They want to
build a bridge and roads so that the people can travel back and forth easily
between the two towns. But they do not have much money, so they hire a
mathematician to calculate where the least expensive place to build the bridge
would be (that is find the shortest route).
Assume
the bridge is to be constructed perpendicular to the river and the river is of
fairly constant width in this location. Also assume that the roads go directly
from the towns to the bridge.
If
you were the mathematician that they hired where would you put the bridge and
why?
One way to see how to
solve this puzzle is to make the roads from Uptown to the bridge and from
Downtown to the bridge parallel by moving the location of the bridge.
Why
does this work?
Another
way is to move the bridge to the beginning of the road from Uptown to the
bridge by using a parallelogram. Then all you need to do is make a straight
line from the end of the moved bridge to Downtown.
Notice
that this also makes the roads parallel?
B. What
if there are two branches of the river between the towns, how would you find
the shortest route in this case?
Using the above ideas
we only need to make all roads parallel.
Have
fun!
Send
your comments, ideas and solutions before Monday to the email below, and
in the subject line be sure to put
MM in the subject line
Visit
us here online at:
http://www2.potsdam.edu/parksjm/MM1.1.htm
to see the results every Friday.
See you next time on MATH MINUTE! (theme music fades out here).