Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2011 Grade 6 Measurement
Problem
Solution
1) When Daisy was on vacation in California, she took a picture of herself in front of a giant redwood tree. She is 5 feet 4 inches tall. In the picture she is 2 inches tall. The tree is 3 inches wide in the picture. What is a good estimate for the circumference of the real tree? Express your answer in whole numbers of feet. Use = 3.14 if needed. 1. Find the ratio of Daisy's height to the height in the picture =
    5 x 12 + 4 = 64 in/2 in = 32
2. Apply this ratio to the tree's width in the picture. Tree width =
    3 x 32 = 96 in.
3. Using this as a circular diameter, D, compute the circumference of the tree =
    C = D = 96 x 3.14 = 301.44 in/12 = 25.12 = 25 ft.
2) Nadia wants to run a marathon in June. When she started training in early March, she could only run for 15 minutes and go a distance of one mile in that time. By early April she was running for 35 minutes at a time and her speed had gone up by 30%. How far did she run per day in early April? Round to the nearest tenth of a mile.
 1. Nadia's speed in March is 15 min/mile.
2. Using this, compute her speed in April = 15/1.3 = 11.538 min/mile.
3. Divide her April running time by her new speed to get the distance she ran = 35 min/11.538 min/mile = 3.03 miles = 3 miles

Problem
Solution
3) A regular sheet of 8 1/2 x 11 inches piece of paper is folded in two different ways to make a square prism with missing ends. See diagram for fold lines, diagram is not to scale. If you add the missing square ends to each prism by cutting them out from other paper, what is the difference in surface area between the two prisms? Express your answer as a mixed number or rounded to the nearest tenth.
1. For the prism made from the first picture, folded along the 8 1/2 inch side, the sides of the end square are 8.5/4 = 2.125 in.
2. Compute the surface area of this prism, adding the 2 missing square ends =
    11 x 2.125 x 4 + 2 x 2.1252 = 102.53 sq. in.
3. For the prism made from the second picture, folded along the 11 inch side, the sides of the end square are 2.75 in.
4. Compute the surface area of this prism, adding the 2 missing square ends =
    8.5 x 2.75 x 4 + 2 x 2.752 = 108.625 sq. in.
5. Take the difference between these 2 surface areas =
    108.625 - 102.53 =
    6.095 sq. in. rounded = 6.1 sq. in.
4) Murphy's living room is 12.5 x 21 feet. He is buying new wall to wall carpet that costs $89/square yard and wants to have the minimum of scrap left over. You can only buy whole numbers of square yards. How much will he pay for the carpet? 1. Convert the room's measurement to yards =
    4.1667 x 7. = 29.16667 sq. yds
    rounded up = 30 sq. yds.
2. Multiply by the cost/yard of the carpeting =
    30 X $89 = $2670
5) In a school Minute to Win It contest two contestants need to take water from one bucket to a container on a scale 25 feet away using a tablespoon. Whoever has the most water on their side of the scale at the end of a minute wins. Naomi carefully carries a full tablespoon across every time going at an average speed of 3 ft/sec. Her return speed is 15 ft/sec with no waiting. Tori goes as fast as she can in both directions at an average speed of 12 ft/sec with no waiting but she spills water and is left with 1/3 tablespoon to put in her container each time. At the end of the minute who brought over more water and by how many tablespoons? 1. Compute Naomi's round trip time to the bucket and back =
    25/3 + 25/15 = 8.333 + 1.6667 sec = 10 sec.
2. Compute Tori's round trip time to the bucket and back =
    25/12 + 25/12 = 4 1/6 sec.
3. Compute the number of tablespoons Naomi delivers:
    60/10 = 6 tablespoons.
4. Compute the number of tablespoons Tori delivers:
    (60/(25/6))/3 = 4.8 tablespoons
5. Naomi brought over more tablespoons by
    (6 - 4.8) = 1.2 tablespoons