Problems 1 through 4 of 2008 Team Round #3

These are just hints:

1) The total number of sandwiches can be divided by 7 with nothing left over. Divide total by 7, multiply the result by 2.

2) L = 4/3 W Area is LW (note: LW means L times W) LW = 300, but when you substitute L=4/3 W, you get a formula for W squared. Take the square root, you know W. Then use L=4/3 w to get L. Note: the problem asks for "length."

3) The smallest 3-digit number divisible by 11 is 110. Since 110 is divisible by 2 with nothing left over, it can't be the answer. Try 121, it meets all the conditions.
Another way, the answer has to be 1 plus a multiple of 60. It can't be 61, because 61 is not a 3-digit number. But it could be 120 plus 1, or 121. This is "educated guessing" I don't know any other way to do it. "Sixty" is the least common multiple of 2,3,4,and 5.

4) When an elevator goes from first floor to third floor, it really goes up 2 "spaces:" draw a picture. So, when it goes from first floor to 20th floor, it goes up 19 spaces.

Watching Planet Venus

You go out at a specified time and watch Venus.
How long can you watch until Venus
sets? On a scale with North 0, East 90, South 180
and West 270, show where Venus sets, if possible,
show a local landmark.

Times are given for Mendota Heights, MN but are
accurate for Minneapolis as well. See worked example
at the end of the data.



Data below!






















MENDOTA HEIGHTS, MINNESOTA                  
Location:  W 93°07'48.0", N44°53'24.0",            
(Longitude referred to Greenwich meridian)          

Time Zone:  6h 00m west of Greenwich (Central Standard Time)             

  Date                       Set  Azimuth Begin observing at
 (Zone)                          h  m   °      h  m
 
2009 Feb 01 (Sun)                21:25 272     19:45

2009 Feb 02 (Mon)                21:26 273     19:30

2009 Feb 03 (Tue)                21:26 274     19:45
         
2009 Feb 04 (Wed)                21:27 274     19:30
         
2009 Feb 05 (Thu)                21:28 275     19:45
         
2009 Feb 06 (Fri)                21:28 276     19:30
         
2009 Feb 07 (Sat)                21:28 276     19:45
         
2009 Feb 08 (Sun)                21:29 277     19:30
         
2009 Feb 09 (Mon)                21:29 277     19:45
         
2009 Feb 10 (Tue)                21:29 278     19:30
         
2009 Feb 11 (Wed)                21:29 279     19:45
         
2009 Feb 12 (Thu)                21:29 279     19:30
         
2009 Feb 13 (Fri)                21:29 280     19:45
         
2009 Feb 14 (Sat)                21:29 280     19:30
         
2009 Feb 15 (Sun)                21:28 281     19:45
         
2009 Feb 16 (Mon)                21:28 281     19:30
         
2009 Feb 17 (Tue)                21:27 282     19:45
         
2009 Feb 18 (Wed)                21:27 283     19:30
         
2009 Feb 19 (Thu)                21:26 283     19:45
         
2009 Feb 20 (Fri)                21:25 284     19:30
         
2009 Feb 21 (Sat)                21:24 284     19:45
         
2009 Feb 22 (Sun)                21:22 284     19:30
         
2009 Feb 23 (Mon)                21:21 285     19:45
         
2009 Feb 24 (Tue)                21:19 285     19:30

2009 Feb 25 (Wed)                21:18 286     19:45
         
2009 Feb 26 (Thu)                21:16 286     19:30
         
2009 Feb 27 (Fri)                21:14 287     19:45
         
2009 Feb 28 (Sat)                21:11 287     19:30

Example: suppose I begin observing at 19:30 on February 1. Venus sets at 21:25.
I can't subtract 30 from 25, so I "borrow" an hour from 21, an hour is 60 minutes.
Now I am subtracting 19:30 from 20:85. Subtracting hours from hours & minutes
from minutes, I observe for 1 hour and 55 minutes. The sun sets at angle 272 degrees,
which is just a little north of west, behind the houses on the opposite
side of the street. (Note: I will observe tonight and improve this).
         

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