Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2012 Grade 8 Measurement

Problem
Hint
1) Four year old Tyrol sleeps 10 hours and 30 minutes each day. If he does that for a whole year that is 365 days long, how long is that to the nearest minute expressed in days, hours, and minutes? Compute the total hours of sleep in a year and then convert that into days, hours and minutes:


______days ______ hours _____ minutes ______
2) The dimensions of a gaming room are 10 feet by 17 feet by 11 feet. A spider and a fly are both in the room. What is the furthest distance they could be apart to the nearest tenth of a foot? The longest distance they can be from each other is from an upper corner of the room to the lower opposite corner. Apply the pythagorean theorem twice to figure this distance:








d = ________ feet.
3) Mario is driving in Canada at a steady rate of 100 km/hr. His twin sister, Daneka, is driving at a steady rate of 70 mph in Washington. Who is faster and by how much? Express your answer in mph. Note 1 mile = 1.609 kilometers. Multiply the rate Mario is driving by the inverse of the conversion factor (to make sure the units cancel properly) to get the speed in mph:


= ____________ mph.

Problem
Hint
4) Donte is mowing his lawn. The front wheels of the mower are 5 inches in diameter and the back wheels are 8 inches in diameter. Donte begins by pushing the mower for 48 feet along the front edge of his lawn. How many more rotations will each front wheel make than each back wheel over the 48 feet? Round your answer to the nearest tenth of a rotation. Compute the circumferences of both wheels and divide the 48 feet by each of these to determine the number of revolutions of each wheel. Then subtract the 2:






= _______ more revolutons of the front wheel.
5) Suppose it were always true that 7 cats can catch 7 mice in 7 minutes. How many cats would it take to catch 100 mice in 50 minutes?
  1. It takes ___ minutes for 1 cat to catch a mouse.

  2. So, in 50 minutes 1 cat can catch _____ mice.

  3. So to catch 100 mice would take _______ cats.