News from Mathnasium of Middletown KY
Problem of the Week 08-15-16
Aug 16, 2016
Question: The South Korean handball team scored 28 points against the Swedish handball team. The Swedish team won by 3 points. How many points did the Swedish team score in total?
Answer: 31 points
Solution: If the Swedish team won by 3 points, then they scored 3 more points than the South Korean team. So, the Swedish team scored 28 + 3 = 31 points.
Question: Anna, Kristin, and Olga each won a medal in Olympic cycling. The cyclist in first place won the gold medal, the cyclist in second place won silver, and the cyclist in third place won bronze. Kristin placed 2 positions higher than Anna. Match the medals to their winners.
Answer: Kristin won gold, Olga won silver, and Anna won bronze.
Solution: If Kristin positions higher than Anna, then she must have won gold because 1st place is the only available position that’s 2 places higher than another. Anna must therefore be in 3rd place, winning bronze. That leaves the silver medal for Olga in second place.
Question: Ding Ning won the gold medal in Olympic table tennis. She was one of 32 players in Round 3 of the competition. Each consecutive round of table tennis, 50% of the players were eliminated. How many games of table tennis did Ding Ning win to make it to the finals if she entered the competition in Round 3?
Answer: 4 games
Solution: After Ding Ning won 1 game, there were 16 opponents left. After she won her second game, there were 8 left. After she won her 3rd game, there were 4 players left. After she won her 4th game, there were only 2 players left in the running for the gold medal. So, Ding Ning won 4 games to get to the finals. Another way to think of this is that in order to reach 2 players, we need to find half of a half of a half of a half of 32. The number of players is reduced by a half four times.
Algebra and Up:
Question: It takes an Olympic canoe paddler 1 minute and 20 seconds to paddle a 300 meter course in the direction of the current. If the current moves at a rate of 1.5 meters per second, then how fast can the paddler paddle in still water?
Answer: 2.25 meters per second
Solution: The speed at which the paddler paddles the course is his own paddling speed, plus the rate of the current. If he paddles 300 meters in 80 seconds, then he’s moving 3.75 meters per second. So, 3.75 mps is equal to his own paddling plus the 1.5 mps the current is pushing him: 3.75 = P + 1.5. P, the rate at which the paddler paddles, is therefore 2.25 meters per second.
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