Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2014 Grade 5 Algebra
Problem
1) You visit the Grand Canyon and drop a penny off the edge of a cliff. The distance the penny will fall is 16 feet the first second, 48 feet the next second, 80 feet the third second, and so on. What is the total distance the penny will fall in 6 seconds?

2) The distance from Spokane to Pasco by train is 150 miles. The train ride is direct with no stops along the way except that the train stops every 30 miles to let freight trains pass. The trip takes 2 hours and 40 minutes. Suppose its average speed is 100 mph. What is the average wait time for letting freight trains pass? Express your answer to the nearest second.

3) In May of 2000, I was eleven times as old as my son, Taylor. Nine years later I was six more than three times his age. How old was Taylor in May 2000?

Problem
4) Rosie has a prime location for a lemonade stand in front of her house and she rents it out when she isn't using it for $5 an hour. Chadd decides to try it. He borrows $10 worth of supplies from his mom that he'll have to pay back, and decides to charge $1 per cup. What should his average selling rate of cups per hour be if he wants to make a profit of $30 in 4 hours?

5) In the pattern of circles shown, each new encircling layer adds more circles. The layers alternate in color beginning with white, then grey, and then white. How many circles will be in the next white layer?