Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2010 Grade 7 Measurement
Problem
Solution
1) Dorey goes to Italy and Greece every year for about half the year. The European currency is the euro with symbol €. She brings back clothing to sell. At the beginning of her trip the dollar to euro exchange rate is $1.00 = € 0.66. She buys silk shirts at € 35 a shirt. How much is that in dollars? The equation is:
  1 dollar x 35 euros = 35/0.66 = $53.03
  0.66 euros

Notice the equation above results in the euro units canceling to make the result dollars. When deciding whether to multiply or divide by the conversion factor you have, make sure the units cancel to make the units you want in the answer.
2) Mrs. Marchinson asks Joey to fertilize the lawn according to the direction on the bag and gives him the bag of fertilizer. He uses a spreader to spread the whole bag evenly over the whole lawn. The bag says to apply 5 lbs/1000 sq ft. and it is a 20 pound bag. Her lawn measures 60 ft by 30 ft. To the nearest whole number percent, by what percent did he over fertilize her lawn?
  1. Mrs. Marchinsonls lawn has an area of
    60x30 = 1800 sq. ft.
  2. The bag can cover 1000x(20/5) = 4000 sq. ft.
  3. He overfertilized by 4000/1800 = 2.22 = 222%
  4. So he overfertilized by 222 - 100 = 122%

3) A conical filter (see picture) is being used to filter sediment from some dirty water out of a stream. The height and diameter of the right circular cone are both 8 centimeters. In one minute the water level in the cone drops from 8 centimeters to 6 centimeters. How much dirty water has been filtered? Express you answer to the nearest tenth of a cubic centimeter.
Volume of a cone is 1⁄3 r2 h.
r is the radius and h is the height. Use = 3.14
  1. Volume of water filtered =
    volume of 8 cm cone - volume of 6 cm cone.
  2. 8 cm cone volume = 8x16 / 3
  3. 6 cm cone volume = 6x9 / 3 =
  4. ( / 3) x (8x16 - 6x9) =
  5. 74 x ( / 3) = 77.5 cu. cm.

Problem
Solution
4) A turtle is racing a hare. The turtle trundles along at a rate of 40 ft per hour without resting. The hare hops along at a rate of 60 ft per hour but rests for 15 minutes every 25 feet. How far into the race does the turtle catch up to the hare the first time? Express your answer rounded to the nearest tenth of a minute. The graph to the right shows the progress of the tortoise and the hare.
  1. At 25 minutes, when the hare takes a break, the tortoise has gone
    40 ft/60 min x 25 min = 16.67 feet.
  2. The hare rests for 15 minutes while the tortoise continues to advance at the same rate, so the time for the tortoise to get to 25 feet is:
    (25 - 16.67) ft /40 ft/60 min = 12.5 minutes which is less than the hare's wait time, so the time the tortoise catches up is:
    25 + 12.5 = 37.5 min
5) Lena and Tully are racing carousel horses. Lena's horse is located 8 feet from the exact center of the carousel and Tully's horse is located further out at 15 feet from the exact center of the carousel. Tully says his horse moves the fastest relative to watchers not on the carousel. The carousel does 4 revolutions per minute. Whose horse moves the fastest in feet per minute and how much faster? Express your answer to the nearest feet per minute.
Use = 3.14
  1. One revolution of Lena's horse = 16 feet
  2. One revolution of Tully's horse = 30 feet
  3. Lena's horse's speed = 4x16 feet per minute
  4. Tully's horse's speed = 4x30 feet per minute
  5. Tully's horse is faster by (120 - 64) feet/min =
    176 feet/min