Math Problem Monday - September 14th, 2020 | Mathnasium Livermore, CA

Lower Elementary:
Question: Today, Jenny picked 8 flowers. Yesterday, she picked 3 more flowers than she picked today. How many total flowers did Jenny pick yesterday and today combined?
Answer: 19 flowers
Solution: Today Jenny picked 8 flowers and yesterday she picked 3 more than today. So Jenny picked 11 flowers yesterday (8 + 3 = 11). Because we want to know how many total flowers she picked for the two days, we add the flowers picked today and yesterday together:
8 + 11 = 19 flowers.

Upper Elementary:
Question: Jenny filled a 5 gallon bucket halfway with water. Then, Jimmy poured 3½ quarts of water into the same bucket and Jaden added a pint of water to the bucket. How much water was in the bucket?
Answer: 3½ gallons
Solution: Since Half of 5 is 2½, Jenny poured 2½ gallons of water in the bucket. Jaden added a pint of water which is half of a quart (2 pints = 1 quart, 1 pint = ½ quart). Adding Jaden’s half quart and Jimmy’s 3½ quarts gives us 4 quarts which is 1 gallon. With Jenny’s 2½ gallons and Jimmy and Jayden’s combined 1 gallon there is a total of 3½ gallons (2½ gallons + 1 gallon) in the bucket.

Middle School:
Question: 500,000 gallons of fuel is used to propel a space shuttle 327,360 feet into outer space. If a particular hybrid car can travel 50 mpg, how many times farther than the shuttle can this hybrid car travel with the same amount of fuel?
Answer: 403,225.8 times farther
Solution: By dividing 327,360 by 5,280 we find that the shuttle propelled 62 miles into outer space. With 500,000 gallons of fuel, and assuming the hybrid car never breaks down, the hybrid car can travel 25,000,000 (500,000 × 50) miles. Finally, by dividing 25,000,000 miles by 62 miles, we find how many times farther the hybrid travels with the same amount of fuel.
25,000,000 ÷ 62 = 403,225.8

Algebra and Up:
Question: On still water, a particular boat travels at 15 mph. If it takes 19 minutes for this boat to travel up stream to a certain spot, and 11 minutes to travel downstream to where it started, how fast is the river’s current?
Answer: 4 mph
Solution: This problem can be solved by using the formula d = rt (distance equals rate times time). Let r_b equal the rate of the boat in still water and r_cbe the rate of the river current.
Upstream:
d = r₁t₁ = (r_b – r_c)t₁
Downstream:
d = r₂t₂ = (r_b + r_c)t₂
Because the distance upstream is the same as the distance downstream we can set the two equations equal to each other.
(r_b – r_c)t₁ = (r_b + r_c)t₂

Now we substitute known values and solve.
(15 – r_c)19 = (15 + r_c)11

285 – 19r_c = 165 + 11r_c
120 = 30r_c
r_c = 4