Answers to Problems of the week- August 3 to August 7

Rewards for Problems of the week:

5 points for the correct answer at your level; 10 points for the next level; 20 points each for 2+ levels up. 

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.

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 = â…” of the mornings it quacks. Since ¾ is more than â…”, the alarm clock is more effective than the duck.

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.

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.

Challenge problem to take home. 20 points for the correct answer. 

Zachary travels on a journey of 50 miles. He spends half of his time riding his horse and half of his time walking. When he rides his horse, he covers 9 miles every hour. When he walks, he covers 3 miles every hour. How much time does it take him to complete the journey?

Answer: 8 hours.