Problems of the Week – March 5 to March 9

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: A sheepdog has a litter of 7 puppies and 1 adopted piglet. Each puppy eats 2 cups of food per day. The piglet eats twice as much as a puppy. How many cups of of food do the baby animals need each day in total?
Answer: 18 Cups
Solution: Since each of the 7 puppies eats 2 cups of food each day, all of the puppies eat 2, 4, 6, 8, 10, 12, 14 cups of food in a day. The piglet eats twice as much as a puppy, and twice as much as 2 cups is 4 cups. So, the baby animals eat 14 + 4 = 18 cups of food in total.

^[6]Upper Elementary:
Question: One farmer sleeps through his alarm clock 3 times every 12 days. Another farmer has a duck that wakes him up 2 out of every 3 days by quacking. Which wakeup method is more effective, the alarm clock or the duck?
Answer: The Alarm Clock
Solution: Since the farmer sleeps through his alarm 3 times every 12 days, he wakes up to his alarm clock 9 times every 12 days. So, the alarm clock is successful 9 ÷ 12 = ¾ of the mornings it’s used. The duck wakes up the farmer 2 ÷ 3 = ⅔ of the mornings it quacks. Since ¾ is more than ⅔, the alarm clock is more effective than the duck.

^[7]Middle School:
Question: Esme makes a dollhouse that is a perfect miniature of her own farmhouse. The farmhouse is 12 yards wide. The dollhouse is 18 inches wide. What are the dimensions of a miniature refrigerator that goes inside the dollhouse if the real-life refrigerator in the farmhouse is 3 feet wide, 2 feet deep, and 5 feet tall?
Answer: 1½ inches × 1 inch × 2½ inches
Solution: Twelve yards is 36 feet, and 18 inches is 1½ feet. So, the dimensions of the farmhouse are 36 ÷ 1½ = 24 times the dimensions of the dollhouse. To find the dimensions of the miniature refrigerator, we divide by 24:
3 feet (36 inches) divided by 24 is 1½ inches.
2 feet (24 inches) divided by 24 is 1 inch.
5 feet (60 inches) divided by 24 is 2½ inches.

^[8]Algebra and Up:
Question: A pig and a border collie are competing in a sheep herding competition. When the pig approaches the sheep at a rate of 11 mph, the sheep walk away at a rate of 3 mph. When the border collie chases the sheep at a rate of 25 mph, the sheep run away at a rate of 20 mph. Which animal catches up to the sheep faster?
Answer: The Pig
Solution: The distance between the pig and the sheep closes at a rate of 11 – 3 = 8 miles per hour. The distance between the border collie and the sheep closes by 25 – 20 = 5 miles per hour. Since the distance between the pig and the sheep closes faster than the distance between the border collie and the sheep, the pig catches up faster.