Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2014 Grade 7 Measurement
Problem
Hint
1) Hans, an exchange student, calls home and tells his mom that it was 24 degrees Fahrenheit that morning but that it is now 60 degrees Fahrenheit. She's a little confused because she doesn't know the Fahrenheit scale, only Celsius. To explain how big a change this is to her he does some converting. What does that change in temperature correspond to in Celsius if the formula is
    F = 9/5C + 32?
Give your answer to the nearest degree in Celsius.
  1. First, turn the equation around to be an equation for the conversion of Fahrenheit to Celsius:


        C = _______________
  2. Convert the 2 Fahreheit temperatures to Celsius and determine the difference between them:




        Change = ______ degrees Celsius

2) A glass has a height of 12 cm and an inside diameter of 6 cm. Another glass has the same volume but its radius is a third, or about 33.3%, larger. What is the height of the other glass to the nearest centimeter?
  1. Compute the volume of the first glass:


        V = _________
  2. The radius of the second glass is ______ cm.
  3. From this volume, compute the height of the second glass:



        h = ____ cm.

Problem
Hint
3) Tania enters a 26.2 mile marathon. She checks out the course one weekend and it takes her about 4 hours and 24 minutes to run the course. She ran at an average rate of 10 minutes per mile for the first hour, then increased her speed to 9 minutes per mile for the next 36 minutes. She repeated this 10 minutes per mile for an hour, then speeding up to 9 minutes per mile for 36 minutes and slowing back down to 10 minutes per mile for an hour. What was her average speed for the remainder of the course? Give your answer in tenths of a minute per mile.
  1. Compute the time it takes Tania to run that first hour and 36 minutes :


        _____ hours
  2. Multiply that by 2 = _____ hours for 2 cycles
  3. Compute the remaining time after these 2 repetition cycles =


    _____ hours left
  4. Compute the distance left in the marathon


    = _____ miles
  5. Compute the average speed for this remainder = _____ min/mile
4) A water tank has the shape of a rectangular prism with a base of 2000 sq. cm. This tank is being filled at the rate of 12 liters per minute. Find the rate at which the height of the water in the tank increases. Express your answer in millimeters per second. 1 cm3 = 1 milliliter of water. The problem is to find the height of 12 liters of water in the 2000 sq. cm. base tank.
  1. Compute the volume (in cm3) of the 12 liters of water


    = _______
  2. Compute the height in the tank of this volume


    h = _______________ cm.
  3. Convert this height to mm/sec


    = ______
5) Two runners, Jo and Doyle, run on the same oval track. Jo does 2 laps around the track in 26 minutes. Doyle does 5 laps around the track in 35 minutes. If Jo and Doyle both cross the finish line marker on the track now, when would they both be together at the finish line on the track again if they both kept running?
  1. Jo runs one lap in ___ minutes

  2. Doyle runs one lap in ___ minutes

  3. The least common multiple of these 2 times is _____ minutes