Problems of the Week – February 18 to February 22

Click here ^[1] for the Problem Extension Worksheet version of the Problems of the Week.
Click here ^[2] for an MS Word version of the Problems of the Week.
Click here ^[3] for the Canadian Problem Extension Worksheet version of the Problems of the Week.
Click here ^[4] for a Canadian MS Word version of the Problems of the Week.

^[5]Lower Elementary:
Question: Derek has won 3 awards. Hansel has won 1 award. What fraction of all the awards did Derek win?
Answer: ³/₄
Solution: To find the fraction, we first need to add up all of the awards to find the whole: 3 + 1 = 4. Derek won 3 out of the 4 awards, so the fraction of all the awards that Derek won is ³/₄.

^[6]Upper Elementary:
Question: Gasoline costs $1.45 per gallon. If a car’s gas tank holds 15 gallons in total and is only ¹/₅ full right now, then how much will it cost to fill up the tank?
Answer: $17.40
Solution: If the gas tank is ¹/₅ full, then it will need ⁴/₅ × 15 = 12 gallons of gas to fill it. The 12 gallons of gas it takes to fill the tank costs $1.45 × 12 = $17.40.

^[7]Middle School:
Question: An ant is ¹/₁₆ of an inch tall. A middle school student is 4¹/₂ feet tall. The student goes to a learning center that is 54 feet tall. If we scale by height, then how tall would a learning center for ants be?
Answer: ³/₄ of an inch
Solution: The learning center is 54 ÷ 4¹/₂ = 12 times the height of the student. So, the learning center for ants should be 12 times the height of the ant. Since ¹/₁₆ × 12 = ¹²/₁₆ and ¹²/₁₆ reduces to ³/₄, the learning center for ants would be ³/₄ of an inch tall.

^[8]Algebra and Up:
Question: A man throws a computer off of a platform straight to the ground. It falls 16 feet and hits the ground in ¹/₂ of a second. Consider this equation for vertical distance traveled in terms of initial velocity, time, and acceleration due to gravity (32 feet/second²):

(distance) = (initial velocity)(time) – ¹/₂(acceleration due to gravity)(time)²What is the initial velocity of the computer?
(Hint: The computer is traveling straight down, so the distance it travels is -16 feet in this instance.)
Answer: 24 feet per second straight down
Solution: If we plug all our given values into the equation, we get this:

-16 = x(¹/₂) – ¹/₂(32)( ¹/₂)²If we simplify that equation, we get this:

-16 = x(¹/₂) – 4If we then solve for x, we get -24. The initial velocity of the computer is therefore 24 feet per second straight down.