Course:MATH110/Archive/2010-2011/003/Groups/Group 05/Homework 3

Problems 1-6 Charly Huxford

1. A bus traveled from the terminal to the airport at an average speed of 30 mi/hr and the trip took an hour and 20 min. The bus then traveled from the airport back to the terminal and again averaged 30 mi/hr. However, the return trip required 80 min. Explain.

The bus is traveling the same distance between the terminal and the airport and back to the terminal at the average speed of 30 mi/hr. Therefore there should not be a time difference. Just looking at the times, we will see that one hour and twenty minutes is equal to eighty minutes! (60 minutes + 20 minutes = 80 minutes)

2. A lady did not have her driver's license with her when she failed to stop at a stop sign and then went three blocks down a one-way street the wrong way. A policeman saw her, but he did not stop her. Explain.

The woman was not stopped by the police officer because she was walking. The problem does not say anything about her driving, it only references her drivers license.

3. One of three boxes contains apples, another box contains oranges, and another box contains a mixture of apples and oranges. The boxes are labeled APPLES, ORANGES and APPLES AND ORANGES, but each label is incorrect. Can you select one fruit from only one box and determine the correct labels? Explain.

We know that EVERY box is mislabeled. The box of oranges could be labeled as apples or apples and oranges, and the box of apples could be labeled as oranges or apples and oranges. Therefore, you must take a fruit from the box labeled as "Apples and Oranges". If you get an orange, then that must be the box that contains only oranges. Now the box labeled "apples" cannot contain just oranges, and it cannot be the box that contains just apples. Therefore, the box labeled "apples" contains both apples and oranges and the remaining box will have the apples.

4. I am the brother of the blind fiddler, but brothers I have none. How can this be?

After reading this problem and seeing the word 'brother', we automatically assume that the fiddler is male. However, the problem says nothing about the fiddlers gender. If the man is the brother of the blind fiddler, but he has no brothers, then the blind fiddler must be female. His sister!

5. Two quarters rest next to each other on a table. One coin is held fixed while the second coin is rolled around the edge of the first coin with no slipping. When the moving coin returns to its original position, how many times has it revolved?

The quarter will revolve twice. It will go around halfway on the first revolution, and back to its original position on the second revolution.

6. Three kinds of apples are all mixed up in a basket. How many apples must you draw (without looking) from the basket to be sure of getting at least two of one kind?

You must pick at least 4 apples. If you pick less than 4, it is possible that they will all be different.

Problems 7-13 Megan Bontogon

7. Suppose you have 40 blue socks and 40 brown socks in a drawer. How many socks must you take from the drawer (without looking) to be sure of getting (i) a pair of the same color, and (ii) a pair with different colours?

(i)In order to be sure you have a pair of the same colour you must take 3 socks from the drawer. If you only pick two socks then it is possible that they are different. However if you pick 3, at least 2 of them must be different. (ii)In order to be sure you have a pair with different colours you also need to take 3 socks from the drawer. If you only pick 2 socks then it is possible that they are the same. However if you pick 3 there will be at least 2 that are different.

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.

This is possible if Reuben's birthday is on the 31st of December. On the 30th of December he is still 20 (say it's the year 2000). On January 1st (2001) he says "Two days ago(on Dec. 30, 2000) I was 20 years old. Later next year(2002) I will be 23 years old.” Later that year on december 31st (2001) he'll turn 22, so later NEXT year(2002) he'll be 23.

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?

If 10 rungs are showing each a foot apart there will be 5 rungs showing after the tide rises five feet.

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.

(i)1/2 of all people*1/2 women = 1/4 of people are women chocolate eaters. (ii)If 1/2 of all people are women then 1/2 of all people would be men, therefore 1/4 of people are 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?

This is not possible. For example, say that the worst player's twin was the daughter, so the best player must be male.The worst player must be the son because he is the only other player that could be twins with the daughter. If the best player and worst players are of opposite sex this cannot be possible.

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.

He could have rarely visited because the brooklyn train always arrives a minute before the bronx train every 10 minutes. Ex. The bronx train arrives at 9:00, 9:10, 9:20, etc., while the Brooklyn train arrives at 8:59, 9:09, 9:19, etc.

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)?

If a clock takes 5 seconds to strike 5 times then it takes 1 sec/chime, therefore in order to chime 10 times it will take 10 seconds to chime.

Problems 14-20 Angus McWhirter

14. One day in the maternity ward, the name tags for four girl babies became mixed up. (i) In how many different ways could two of the babies be tagged correctly and two of the babies be tagged incorrectly? (ii) In how many different ways could three of the babies be tagged correctly and one baby be tagged incorrectly?

i) 2 correct ways and 2 incorrect ways ii) 6 correct way and 3 incorrect ways

15. Alex says to you, “I'll bet you any amount of money that if I shuffle this deck of cards, there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck.” Should you accept his bet?

yes, as no matter amount of shuffling will leave an equal amount of red in the first part then there is in the second, as there are only 2 colours (red and black) and there are 26 red cards and 26 black cards, thus an increase in a colour in the first half of the deck will result in an increase in the amount of the opposing colour in the second half of the deck.

16. Suppose that each daughter in your family has the same number of brothers as she has sisters, and each son in your family has twice as many sisters as he has brothers. How many sons and daughters are in the family?

There are 3 brothers and 4 sisters

17. The zero point on a bathroom scale is set incorrectly, but otherwise the scale is accurate. It shows 60 kg when Dan stands on the scale, 50 kg when Sarah stands on the scale, but 105 kg when Dan and Sarah both stand on the scale. Does the scale read too high or too low? Explain. The scale reads too low as in order for Dan and Sarah to both weight 105 kg, the scale must be set back 2.5 kgs so that the combined weight of Dan and Sarah = 105. (60-2.5) + (50-2.5)= 105

18. Alice takes one-third of the pennies from a large jar. Then Bret takes one-third of the remaining pennies from the jar. Finally, Carla takes one-third of the remaining pennies from the jar, leaving 40 pennies in the jar. How many pennies were in the jar at the start?

19. One morning each member of Angela's family drank an eight-ounce cup of coffee and milk, with the (nonzero) amounts of coffee and milk varying from cup to cup. Angela drank a quarter of the total amount of milk and a sixth of the total amount of coffee. What is the least number of people in the family?

20. Of two clocks next to each other, one runs 5 min per hour fast and the other runs 5 min per hour slow. At midnight the clocks show the same time. At what time are they are one hour apart?