Math Problem Monday - June 8th, 2020 | Mathnasium Livermore, CA

Lower Elementary
Question: Kevin, Paul, and Winnie are seeing who can run 100 yards the fastest. Winnie finished 2 seconds before Paul and Kevin finished a ½ of a second before Winnie. If Paul ran 100 yards in 15 seconds, how long did it take for Kevin to finish?
Answer: 12½ seconds
Solution: Starting with Paul and moving backwards, it took Winnie 2 seconds less than Paul to run 100 yards. Since it took Paul 15 seconds, it took Winnie 13 seconds (15 – 2 = 13). Kevin finished a ½ of a second faster than Winnie. A half a second less than Winnie would be 12½ seconds.

Upper Elementary
Question: A full grown giraffe has a heart that is 2 feet long, weighs about 25 pounds, and beats 170 times a minute. How many times will a giraffe’s heart beat in 5 minutes?
Answer: 850 times
Solution: The fact that a giraffe’s heart is 2 feet long and weighs about 25 pounds has no relevance to the actually question being asked. In order to solve this problem we find what 170 five times is.
170 x 5 = 850

Middle School
Question: Benny wants to put carpet in his bedroom, office, and hallway. If his bedroom is a perfect square with sides 25 feet long, his office is a triangle with a base and height of 15 feet, and his hallway is a rectangle with a length of 30 feet and a width of 8 feet, how many square feet does benny need? (Round answers up to the nearest foot.)
Answer: 978 ft²
Solution: To help solve this problem, let’s draw a picture for each room labeling their proper dimensions.

To find how much carpet Benny needs, we find the area of each room and then add all the areas together.

     Bedroom:
          A_B = s² = (25 ft)² = 625 ft²
     Office:
          A_O = ½bh = ½(15 ft)(15 ft) = ½(225 ft²) = 112.5 ft²
     Hallway:
          A_H = lw = (30 ft)(8 ft) = 240 ft²
     Total carpet needed:
          T = A_B + A_O + A_H = 625 ft² + 112.5 ft² + 240 ft² = 977.5 ft²
Rounding up to the nearest square foot gives us 978 ft² .

Algebra and Up
Question: The land speed record is the highest speed achieved by a wheeled vehicle on land. Currently this record is held by Andy Green driving the Thrust SSC. Powered by two turbofan engines the Thrust SSC broke the sound barrier at 763.035 mph. At this speed, how many seconds would it take for the Thrust SSC to travel 100 yards? (Round answer to the nearest thousandths.)
Answer: 0.268 seconds
Solution: The best, most efficient way to solve this problem is to use dimensional analysis.

Because the Thrust SSC, at 763 mph, travels roughly 373.093 yards per second, we divide 100 yards by 373.093 yards per second to find how long it takes the thrust SSC to travel 100 yards.
     100 yd. / 373.093 (yd./sec) ≈ 0.268 seconds.