Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2006 Grade 7 Measurement
Problem
Solution
1) At a slug race, the fastest slug traveled 10 inches per hour, but it had to rest for 30 minutes every 3 feet. At this record setting pace, how long will it take the slug to travel 8 feet? 1. If the slug rests 30 minutes every 3 feet then it rests 2 times in a 8-foot race.
2. Convert the slug's 'speed' to feet/hour = 10/12 = .8333 ft/hr.
3. Multiply the slug's speed by the distance and
    add the rest times = 8 ft. / 0.833 ft/hr + 2 (30 min) =
    9.6 hr + 1 hr. = 10.6 hours. = 10 hours 36 min.
2) Elevators at the Space Needle travel at the same speed as raindrops, 10 miles per hour. The elevator ride takes about 40 seconds. How far, to the nearest foot, will the elevator travel? Note: 5280 feet = 1 mile 1. Convert the elevator's speed to feet/hour =
    10 mi./hr. = 5280 x 10 = 52800 ft/hr.
2. Convert the elevator ride time to hours =
    40/3600 = 0.0111 hours.
3. Muliply this by the time of the elevator ride =
    52800 x 0.01111 = 586.67 feet.
4. Rounded = 587 ft.
3) Sam cuts a piece of wire 64 centimeters in length into two parts. The parts are then each bent to form a square. The total area of the two squares is 130 square centimeters. How much larger is a side of the larger square than a side of the smaller square? The sides of each square are in whole number lengths. This is actually an algebra problem with 2 equations and 2 unknowns
Call the two side lengths a and b.
  1. First equation:    4a + 4b = 64 cm.
  2. Second equation:    a2 + b2 = 130 sq. cm.
  3. First equation reduced by dividing by 4: a + b = 16
  4. First equation as expression for a: a = 16 - b
  5. Substitute in the second equation:
    (16 - b)2 + b2 = 130 sq. cm.
    256 - 32b + b2 + b2 = 130
    2b2 - 32b + 126 = 0
    b2 - 16b + 63 = 0

  6. Using the quadratic formula:
        b = 16 ± √256 +4(63)      = 8 ± 1 = 9 or 7
                      2
  7. So b is 9 or 7 and a is 7 or 9
  8. The larger side is 2 cm. longer than the shorter side

Problem
Solution
4) 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. (12x200) pages/year = 2400/7300 = 24/73 pages/minute
365x20 minutes/year

5) 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 the 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 of boxes Dan can pack into the truck? 		Try to find truck dimensions that fit most evenly with the box dimensions.
  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.