Course:MATH110/Archive/2010-2011/003/Groups/Group 08/Questions 8-13

8.Reuben says, “Two days ago I was 20 years old. Later next year I will be 23 years old.” Explain how this is possible.

• Assume Reubens birthday is December 31st

• On December 31st he turned 21

• It is now January 1st

• 2 days ago was December 30th and he was 20 then

• By the end of this year he will be 22, which means a year from January 1st he will be 23 By using Polyas four step method you can break the information down and write it out making a more clear structure that is easier to read and work through

9. A rope ladder hanging over the side of a boat has rungs one foot apart. Ten rungs are showing. If the tide rises five feet, how many rungs will be showing?

• Know the distance between each run= 1 foot

• 10 rungs are not in the water yet because they are showing

• Tide rises 5feet

• We know from the given information that from the bottom of the ladder to the fifth rung is 5 feet

• Therefore 5 rungs are in the water now Once again Polya’s method helped to breakdown the information step by step and use the method of deduction.

10. Suppose one-half of all people are chocolate eaters and one-half of all people are women. (i) Does it follow that one-fourth of all people are women chocolate eaters? (ii) Does it follow that one-half of all men are chocolate eaters? Explain.

• ½ all people= chocolate eaters

• ½ all people=women

• ½ population=women and ½ population=men

• Therefore, (1/2)(1/2)=1/4 women chocolate eaters and ¼+ ¼= ½ men chocolate eaters

11. A woman, her older brother, her son, and her daughter are chess players. The worst player’s twin, who is one of the four players, and the best player are of opposite sex. The worst player and the best player have the same age. If this is possible, who is the worst player?

• Start with deduction reasoning. You can find that the woman and her brother could possibly be twins, they are of the opposite sex, and they have the same age (even though he is the older brother you don’t know how much older; could be by seconds).

• Son and daughter could be twins, both of opposite sex, and have the same age (but once again you don’t know)

• Therefore, it is not possible to know who the worst player is. Polya’s method helps us to see it could be any one of them according to deductive reasoning and working through the words.

12. A Manhattan fellow had a girlfriend in the Bronx and a girlfriend in Brooklyn. He decided which girlfriend to visit by arriving randomly at the train station and taking the first of the Bronx or Brooklyn trains that arrived. The trains to Brooklyn and the Bronx each arrived regularly every 10 minutes. Not long after he began his scheme the man's Bronx girlfriend left him because he rarely visited. Give a (logical) explanation.

Even though each train arrives regularly every 10 minutes that doesn’t mean that they are arriving at the same time. The Brooklyn train may arrive at 2:00, 2:10, 2:20, 2:30….and the Bronx train may arrive at 2:13, 2:23, 2:33….Therefore, the Brooklyn train was always the first there so he would take that train and rarely took the Bronx one.

13. If a clock takes 5 seconds to strike 5:00 (with 5 equally spaced chimes), how long does it take to strike 10:00 (with 10 equally spaced chimes)?

• 5 seconds to strike 5:00=5 equally spaced chimes

• X seconds to strike 10:00=10 equally spaced chimes

• The answer would be 10 seconds because it doubles