Problems of the Week – November 13 to November 17

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: John is older than Michael. Wendy is older than John. If Michael is 3 years old and Wendy is 12 years old, could John be 120 months old?
Answer: Yes
Solution: There are 12 months in a year, so John must be 10 years old because 12 months 10 times is 120 months. Since 10 years is older than Michael’s 3 years and younger than Wendy’s 12 years, that means John could be 120 months old.

^[6]Upper Elementary:
Question: A fairy can fly 16 miles per hour. If the fairy leaves for Neverland at 8:03 PM and gets there at 7:33 AM, then how far away is Neverland?
Answer: 184 miles
Solution: From 8:03 PM to 7:33 AM is 11½ hours. So, the fairy travels a total distance of 16 × 11½ = 16 × 11 + 16 × ½ = 176 + 8 = 184 miles.

^[7]Middle School:
Question: Wendy and the Lost Boys are taking turns reading each other a bedtime story. Wendy reads 50% of the story. Tootles, Nibs, Slightly, and Curly each read 50% of the number of pages that are left on each of their turns. Finally, the twins each read 50% of the remaining pages. What percentage of the story has been read by the time it’s the twins’ turn to read?
Answer: 96.875%
Solution: After Wendy reads, 50% of the pages are left to read. After Tootles, 50% × 50% = 25% are left. After Nibs, 50% × 25% = 12.5% are left. After Slightly, 50% × 12.5% = 6.25% are left. After Curly, 50% × 6.25% = 3.125% are left. So, by the time it’s the twins’ turn to read, 3.125% of the pages are left, which means 100% – 3.125% = 96.875% of the story has been read.

^[8]Algebra and Up:
Question: A swimmer is 20 meters from a boat. A crocodile is 30 meters behind the swimmer. If the crocodile swims 4 meters per second and the swimmer swims 2 meters per second, will the crocodile catch the swimmer before he reaches the boat?
Answer: No
Solution: The crocodile swims 4 – 2 = 2 meters per second faster than the swimmer. So, the crocodile gets 2 meters closer to the swimmer each second. It takes the swimmer 20 meters ÷ 2 meters per second = 10 seconds to reach the boat. In that time, the crocodile gets 10 seconds × 2 meters per second = 20 meters closer to the swimmer. Since they were 30 meters apart to begin with, the crocodile does not catch the swimmer.