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: The year is 2018. A time traveler transports himself 40 years back in time, then 20 years forward in time, then 34 years back in time. What year is it for the time traveler now?
Answer: 1964
Solution: Forty years before 2018 is 2018 – 40 = 1978. Twenty years after that is 1978 + 20 = 1998. Thirty-four years before that is 1998 – 34 = 1964. So, it is 1964 for the time traveler when he stops traveling through time.
[6]Upper Elementary:
Question: Rose works for Henrik’s department store where she makes $9.00 per hour. She begins her workday at 8:00 AM and intends to work for 4 hours, but is interrupted at 9:30 AM when aliens attack. How much more money would Rose make if she were able to work her full 4-hour shift?
Answer: $22.50
Solution: Rose works for 11/2 hours from 8:00 am to 9:30 am instead of the 4 hours she intends to work. So, she misses 4 – 11/2 = 21/2 hours. In 21/2 hours, she would have made 21/2 × $9.00 = $22.50.
[7]Middle School:
Question: Mickey the mechanic can replace the tires on a car in 20 minutes. His friend Noel can replace the tires on a car in 25 minutes. If they work together and only one person can work on a tire at a time, how long will it take them to replace all 4 tires on a car?
Answer: Either 121/2 or 12 minutes, depending on how you solve the problem
Solution: There are two ways to solve this problem. First, Mickey and Noel can each replace half of the wheels. Mickey can replace 4 wheels in 20 minutes, so he can replace 2 wheels in 10 minutes. Noel can replace 4 wheels in 25 minutes, so he can replace 2 wheels in 121/2 minutes. If they work at the same time, they’ll be done in 121/2 minutes. Alternatively, we can find out how long it would take them if Mickey takes over for Noel after 10 minutes, at which point Noel will be 10 ÷ 121/2 = 4/5 done with his half of the tires. Since Mickey can finish 2 tires in 10 minutes, he can finish the remaining 1/5 of Noel’s work in 1/5 × 10 = 2 minutes. So, if Mickey takes over, they can get the job done in 12 minutes.
[8]Algebra and Up:
Question: The planet Gallifrey has a radius of about 3,000 miles. Earth has a radius of about 4,000 miles. How many cubic miles greater is the volume of Earth than the volume of Gallifrey? Round π to 3.14 and your answer to the nearest cubic mile.
Answer: 154,906,666,666 miles3
Solution: We use the formula 4/3πr3 to find the volume of each planet. Earth’s volume is approximately 267,946,666,666 miles3, and Gallifrey’s volume is 113,040,000,000 miles3. The difference is therefore 154,906,666,666 miles3.