Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2015 Grade 6 Measurement
Problem
Solution
1) A children's park is being constructed and will require rubber, bark, and soil for various play areas. Only a single material is used in a play area. The park needs twice as much rubber as bark, and three times as much soil as rubber. If the play areas require a total volume of 36,000 cu. ft. of material, how much soil is needed? 1. Assume 1 unit of bark.
2. Then the park requires 2 units of rubber.
3. The park requires 6 units of soil.
4. The total number of units is 9
5. Soil is 2/3% of the units.
6. Multiply this by the volume of the play area =
    (2/3) x 36000 = 24,000 cu. ft. of soil.

2) It takes six hours by plane that travels at 180 mph (miles/hour) to reach your destination. On the flight back, you take a jet that travels 540 mph (flying the same distance each way). What was your average speed for the round trip?		 Careful! the answer is not (180 + 540)/2!

1. Compute the distance traveled by the first plane =
    180 m/hr x 6 hr = 1080 miles.
2. Compute the time for the return trip =
    1080 m/540 m/hr = 2 hr.
3. Compute the average speed as 2 times
the trip length divided by the sum of the two trip times =
    (2 x 1080) / (6 + 2) = 270 miles/hr.
3) Kaylee is having a party with 22 guests. She orders a sub sandwich that is 5.75 ft long. If she wants to divide the sandwich equally among everyone attending the party (including herself),what will the length of each piece be, in inches? 1. Convert the sub length into inches = 69 in.
2. Divide this by the number of guests
    (plus 1 for herself) = 69/23 = 3 in.

Problem
Solution
4) Abraham, Becca, and Cory are being paid $100 to manage a garage sale for a friend. They all work for 6 hours, except Becca, who has to leave 45 minutes early. If they are dividing the money evenly based on how much time they worked, what is Cory's fair share?
(Round your answer to the nearest cent)		 1. Compute the total number of hours worked as Abraham's, Cory's and Becca's reduced time =
    2 x 6 + 5.25 = 17.25 hrs.
2. Convert $100 to cents = 10,000 cents
3. Divide this by the total number of hours worked by all 3 =
    10000/17.25 = 579.71 cents/hr.
4. Cory's share is 6 x 579.71 = 3478 cents = $34.78

5) An unusual vendor likes to exchange his fruit only for other types of fruits. His exchange rates are: 3 apples for 2 oranges, 5 oranges for 24 grapes, 32 grapes for 6 bananas, and 3 bananas for 5 lemons. How many apples can you get for 30 lemons?		 Work this problem backwards:
1. If 3 bananas = 5 lemons, then 30 lemons =
    6 x 3 =18 bananas
2. If 32 grapes = 6 bananas, 18 bananas = 96 grapes
3. If 5 oranges = 24 grapes, 96 grapes = 20 oranges
4. If 3 apples = 2 oranges, then 20 oranges = 30 apples