Answers to Problems of the Week - August 9 to August 15

Rewards for Problems of the week:

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

Lower Elementary:

Question: A whale shark weighs 20 tons. A car weighs 2 tons. How many cars weigh the same as a whale shark?

Answer:  10 cars

Solution:   We can solve this problem by counting by 2s: 2 tons, 4, tons, 6 tons . . . we’ll find that we need to count 2 tons, 10 times to reach 20 tons. Another way to solve this is to divide 20 tons by 2 tons to find how many times 2 goes into 20: 20 ÷ 2 = 10.

Upper Elementary:  

Question: A baby green sea turtle weighs 4 ounces. A fully grown green sea turtle weighs 350 pounds. How many times heavier is the fully grown green sea turtle than the baby green sea turtle?

Answer:   An adult green sea turtle is 1,400 times heavier than a baby.

Solution:   A pound is 16 ounces, so 16 ÷ 4 = 4 baby sea turtles weigh a pound. Since 4 babies weigh the same as each pound of fully grown turtle, that means that the whole fully grown turtle weighs as much as 350 × 4 = 1,400 baby turtles. It’s 1,400 times heavier.

Middle School: 

Question: A blue coral and a black coral are the same size. The blue coral grows at a rate of 3 millimeters per year. The black coral grows 8 centimeters per year. How much bigger will the black coral be than the blue coral in 100 years?

Answer:  770 centimeters

Solution:  In 100 years, the blue coral grows 3 mm × 100 = 300 mm, which is equal to 30 centimeters. The black coral grows 8 cm × 100 = 800 cm. The black coral will therefore be 800 – 30 = 770 centimeters bigger than the blue coral.

Algebra and Up: 

Question:  Flying fish can jump out of the water and “fly” through the air to avoid predators. A flying fish’s distance from the water’s surface in decimeters can be calculated with the function f(t) = ^–5t² + 15t, in which t is the number of seconds the fish is out of the water. How high above the water is the fish after 1½ seconds?

Answer:  11¼ decimeters

Solution:  To solve the problem, we evaluate ^–5t² + 15t when t = 1½. We get ^–5(1½)² + 15(1½), which is equal to ^–11¼ + 22½ = 11¼ decimeters.

Challenge problem to take home. 5 stars for the correct answer. 

Two ants sit at the base of a cylindrical can with height 6 cm and circumference 16 cm. They want to get to the point at the top of the can directly overhead, but neither ant is in any particular hurry.

Ant A decides to make 2 complete trips around the can, while Ant B decides to make it 3. Given their respective plans, each ant takes the shortest possible path.

How far does Ant B travel compared to Ant A?

Answer: Ant B travels approximately 1.48 times longer than Ant A