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?

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?

 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?

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?

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?