Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2006 Grade 6 Measurement
Problem
Solution
1) Joe flies from Seattle to New York and back regularly on business. Joe left on Wednesday at 5 am, local time, to go to New York. He arrives at 2:15, local time, in New York on Wednesday, works for 5 hours, leaves at 8 pm, local time, to fly back to Seattle and arrives at 11 pm, local time, Wednesday evening. All time between departure and arrival is considered flying time. The time difference between Seattle and New York is 3 hours. How long was he flying? Give your answer in hours and minutes. 1. Convert all times to New York time.
2. Convert all times to minutes from zero hour Wednesday, New York time.
    depart Seattle     480 minutes (8 am NY time)
    arrive New York 855 minutes (2:15 NY time)
    depart New York 1200 minutes (8 pm NY time)
    arrive Seattle       1560 minutes (2:15 am Thursday, NY time)
3. Total flight time = (855 - 480) + (1560 - 1200) =
    375 + 360 = 735 minutes.
4. Convert to hours and minutes = 12 hours 15 minutes.
2) Alex and Zach meet on a track to do a long distance run. They start running from the same point but Alex begins to steadily pull ahead. The first time that Alex passes Zack is at the starting point when Alex has just complete five laps. If Alex runs one lap in 2 minutes, how long does it take Zach to run a lap? Express your answer in minutes and seconds. 1. If Alex has completed 5 laps then Zack has completed 4 laps.
2. The fraction of Alex's distance this represents is 4/5
3. Divide Alex's lap time by this ratio =
    2 / (4/5) = 10/4 = 2.5 min.
4. Express as minutes and seconds = 2 min. 30 sec.

3) At a slug race, the fastest slug traveled 10 inches per hour, but it had to rest for 30 minutes every 3 feet. At this record setting pace, how long will it take the slug to travel 8 feet?		 1. If the slug rests 30 minutes every 3 feet then it rests 2 times in a 8-foot race.
2. Convert the slug's 'speed' to feet/hour = 10/12 = .8333 ft/hr.
3. Multiply the slug's speed by the distance and
    add the rest times = 8 ft. / 0.833 ft/hr + 2 (30 min) =
    9.6 hr + 1 hr. = 10.6 hours. = 10 hours 36 min.

Problem
Solution
4) Elevators at the Space Needle travel at the same speed as raindrops, 10 miles per hour. The elevator ride takes about 40 seconds. How far, to the nearest foot, will the elevator travel?
Note: 5280 feet = 1 mile		 1. Convert the elevator's speed to feet/hour =
    10 mi./hr. = 5280 x 10 = 52800 ft/hr.
2. Convert the elevator ride time to hours =
    40/3600 = 0.0111 hours.
3. Muliply this by the time of the elevator ride =
    52800 x 0.01111 = 586.67 feet.
4. Rounded = 587 ft.

5) A certain medication comes to a pharmacist in powder form. The pharmacist then needs to add purified water and thoroughly mix the solution before dispensing it to a patient. The instructions say to add 2 milliliters of water for every 5 milligrams of powder. If the pharmacist measures out 20 milligrams of powder, how many milliliters of water should he add to prepare the correct medication for the patient? 		1. Compute the dilution ratio in millileters per milligram =
    2/5 = .4 milliliters/milligram
2. Multiply by by the number of milligrams of powder =
    .4 x 20 = 8 milliliters