Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2006 Grade 8 Measurement
Problem
Solution
1) If you read 20 minutes per day every day and end up reading 12 books of 200 pages each in one year, what is your reading rate in pages per minute? A year has 365 days. Give your answer as a reduced fraction, or as a decimal rounded to the nearest tenth of a page per minute.

 Divide the pages per year by the number of minutes per day, making sure that the units cancel correctly to pages/minute:

12 x 200 pages x 1 day = 120/365 = 24/73 pages/minute
      365 days       20 minutes
2) Dan has to load a truck with television sets. The cargo area of the truck is a rectangular prism that measures 22 feet (long) by 9 feet (wide) by 11 feet (tall). Each television set is packed in a box that measures 30 inches by 24 inches by 18 inches. Dan does not need to worry about orientation of TVs since they are packed really well in their boxes. However he does pack them all in the truck with the same orientation so that they stack neatly. What is the maximum number Dan can pack into the truck?
  1. The length of the truck (22 feet) divides evenly into the width of the box (2 feet) so 11 boxes will fit sideways along the length of the truck bed.
  2. The other 2 dimensions that fit with each other are the width of the truck (9 feet = 108 inches) and the height of the boxes (18 inches), so 6 boxes will fit across the width of the truck.
  3. The other truck dimension (11 feet) must fit with the remaining box dimension (30 inches). 132/30 = 4.4, so 4 boxes fit across the height.
  4. This makes 11x6x4 = 264 boxes that will fit in the truck.

Problem
Solution
3) Kyle needs to fill a large tub with water for his horses. He knows it takes 40 minutes to fill it with a small hose and 20 minutes to full it with a large hose. Because he has to do his homework, he wants to fill the tub as fast as possible. How long will it take him to fill the tub using both hoses? Give your answer in minutes and seconds.

 Choose an easy volume of the tub to work with, like 100 gallons.
  1. Small hose rate = 100 gallons/40 minutes =
    2.5 gallons/minute
  2. Large hose rate = 100 gallons/20 minutes =
    5 gallons/minute
  3. Combined rate = 7.5 gallons/minute
  4. t = 100 gallons/7.5 gallons/minute =
    13 minutes 20 seconds
4) The Hall family's shower uses 6 gallons of water per minute. They have 5 people in their family. Dad, Mom, and Jeff all shower every day. Elaine and Eric shower 4 times per week. If the family uses 1,914 gallons of water per week for showers, how long is the average shower at the Hall's home?
  1. Elaine and Eric use 2x4 = 8 showers/week
  2. Mom, Dad and Jeff use 3x7 = 21 showers/week
  3. Total = 29 showers/week
  4. 1914 gallons x 1 week x       1 minute =
              week     29 showers     6 gallons

    1914 / (29x6) = 11 min/shower
5) Mr. Troy from Soup Co. places a large order of cans that will be 13 centimeters tall and 8 centimeters in diameter. The clerk inadvertently records the 13 centimeters as 15 centimeters so that Mr. Troy gets extra large cans. How much more soup will fit in the new cans than in the ones he ordered? Give your answer in exact form or as a decimal rounded to the nearest hundredth. (He's considering sending the order back.)
  1. Original can volume = 13 42 = 208 cu. cm.
  2. New can volume = 15 42 = 240 cu. cm.
  3. The difference = 32 cu. cm.