Answers to Problems of the Week - March 29 to April 3

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: William has 3 fruit trees in his garden. He picks 8 apples from the apple tree, 6 pears from the pear tree, and 7 limes from the lime tree. How many pieces of fruit did William pick?

Answer:  21 pieces of fruit

Solution:  To find the total, add the apples and the pears, and then add the limes: 8 + 6 = 14. Then, 14 + 7 = 21.

Upper Elementary: 

Question: Harrison has a full 3–gallon watering can. He uses ⁵/₈ of the water on the gardenias in his garden. How much water did the gardenias get?

Answer:  15 pints

Solution:  First we converted the amount of water from gallons into pints be­cause a pint is ¹/₈ of a gallon. Harri­son had 24 pints of water. Then we found ⁵/₈ of 24 and determined Har­rison used 15 pints of water.

 Middle School:

Question: Lily is making labels for the plants in her garden. Each label is made of a white 3" × 5" laminated against a colorful 5" × 8" card. What is the area of the front of each label that isn’t covered by the white card?

Answer:  25 square inches

Solution:  First, we need to find the area of the larger card. That’s 5 × 8 = 40 square inches. Next, we subtract the part that’s covered by the white card, which is 3 × 5 = 15 square inches. Then we subtract the area of the small card from the larger card, which gives us 40 - 15 = 25 square inches.

Algebra and Up: 

Question: Cameron is selling flowers from his garden. By selling large bouquets for $21 and small bouquets for $15, he makes $540. If he sells a total of 30 bouquets, how many large bouquets did Cameron sell?

Answer:  15 large bouquets

Solution:  We can use the equations 21L + 15S = 540 and L + S = 30 to solve for both variables. First, we solve for S in the second equation. That gives us that S = 30 – L. We can plug that val­ue of S into the original equation, so 21L + 15(30 – L) = 540. If we solve for L, we get 15.

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

John is observing two trains, yellow and blue, heading towards each other on parallel tracks. They start passing by each other exactly in front of him, which lasts $$\SI{20}{\second}.$20\text{s}.$ It takes the blue train $$\SI{10}{\second}$10\text{s}$ longer than the yellow one to pass by John.

If the speed of the yellow train is $$\SI[per-mode=symbol]{30}{\meter\per\second}$30\text{m}/\text{s}$ while the blue train's speed is $$\SI[per-mode=symbol]{20}{\meter\per\second},$20\text{m}/\text{s},$ what is the length of the yellow train?

Answer: 480 meters