Course:MATH110/Archive/2010-2011/003/Groups/Group 18

Math 110/003 - Group 18
Members:	Audrey Chen
	Sifat Hasan
	Caitlin Lastiwka-Farquharson
	Victoria Wall
	Vivian Zhang

Sub-Pages

Basic Skills Project [1]

Homework due October 20th, 2010

I created a page for our homework due tomorrow: http://wiki.ubc.ca/Course:MATH110/003/Groups/Group 18/Homework October 20th, 2010

-Roland

I've moved the page, it was missing the Course: part which means it was created directly inside the wiki and not as a subpage of your group page, which is something the wiki admins don't like that much. By the way, you're allowed to use spaces in the name of your pages.

-- DavidKohler 06:28, 20 October 2010 (UTC)

First Group Wiki Homework

1-5

Victoria Wall

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.

' 'Lets call the terminal T and the airport A. If the bus travelled from T to A at 30mi/hr and it took them one hour and 20 mins to get from T to A at this speed, and there are 60 minutes in one hour, it took the bus 60min + 20min to get to A which is a total of 80min. The bus took 80 min to get from T to A. To get from A to T at the same speed (30mi/hr) it took the bus 80min. 80min = 80 min. This means going from A to T or vis versa at 30 mi/hr it will take the bus 80min.

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 lady was walking. It never says she was driving.

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.

' 'if you selecet from the box APPLES AND ORANGES then you will be able to see the labels if they are correct or not.

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

' 'Since it says that he is the brother of the blind fiddler it does not mean that the fiddle is male, since he has no brothers than the fiddler must be a female.

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?

' 'This is because the moving quarters revolves two full revolutions

6-10

Caitlin Lastiwka- Farquharson

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

' ' To be sure you are getting at least two of a kind, you must select all of the other types of apples, plus two more. Meaning that only once you have selected all of the other apples can you be sure that you will select two of the kind you desire. It can be written like this: x,a x2, b and x3, c, with x representing the quantity of apples. This can be calculated by x2 + x3 +2. X2 representing one of the types of apples, x3 representing the other type and 2 representing 2 of the kind of apples you are trying to select. This is the only way to be sure you are getting at least two of a kind. ' '

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 colour, and (ii) a pair with different colors.

' 'You must take three socks from the drawer to ensure you have a pair that match. This is because if you only select two, one could be brown and one could be blue. Selecting three, ensures that at least two of them will be the same colour. As for part two, you would need to select 41 socks to ensure you had a pair of different coloured socks because if you select 40 or less you could get all the same colour, but selecting 41 ensures you will have at least one pair of mixed colour. ' '

8. Rueben says "Two days ago I was 20 years old. Later next year I will be 23 years old." Explain how this is possible.

' 'It is possible if your birthday is on the 31st of December and today is the 1st of January. This is because on the 30th of December (two days ago) you we’re 20 years old and now you are 21, later this year you will turn 22 on the 31st of December, and therefore 23 the next year.' '

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?

' ' 5 rungs will be showing, because if there are 10 showing now, and they are each a foot apart, then for 5 more rungs to be showing there would need to be an increase in the level of water by 5 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.

' ' No, it does not follow that one-fourth of all people are women chocolate eaters and it does not follow that half of all men are chocolate eaters because are completely independent scenarios. Meaning that the the amount of women there are does not influence the amount of men that will eat chocolate. For example, If 50% of people are women and 50% of the entire population including men and women eat chocolate (arrived at by using the same logic that if 1/4 of women eat chocolate and 1/4 of men eat chocolate), that entire 50% could be comprised of women, meaning that no men eat chocolate disproving the statement.

11-14

Sifat Hasan

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?

The four players (according to age, from oldest to youngest) are: woman's older brother, woman, and the son and the daughter (of the same age). Assuming that the children are of the same age (i.e. twins), the worst player is one of them, since they are the only ones who can have a twin. Assuming that the worst player is the daughter, her brother the son, is of the opposite sex as the woman, therefore the woman is the worst player. However, since the worst and the best player are of the same age, this is not possible, because the twins are of the opposite sex and they are of different genders.

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

Assuming that the Bronx and the Brooklyn train arrive one after the other every 10 minutes, the only logical explanation would be that the man in Manhattan coincidentally went to the station 10 minutes or less before a train to Brooklyn arrived, most of the time.

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 it takes 5 seconds to strike 5, there will be 4 little halts in the middle. Therefore it takes 5 chimes 4 (5/4) = 1.25 second halts to finish. For 10 chimes, there are 9 halts so, it takes 9x 1.25 = 11.25 seconds for 10 halts.

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)and (ii) If we take the babies names as A,B,C and D. There are 6 different combinations of the mix up, that two babies' names can be correct and 2 can be wrong. Assuming the name tags for the babies A,B,C and D are in respective order, they are ABDC, ADCB, ACBD, DBCA, CBAD and BACD. All other combinations for example BCAD will have one correct and 3 incorrect, or all four of them correct, because if 3 are correct, the fourth one has to be correct.

15-16

Roland Will

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?

Answer: No, you shouldn't assuming the deck has equal amounts of red and black cards as in a standard 52 card deck. Solution: In a standard 52 card deck, half of the cards (26) are black and half are red. If you take 26 cards at random from the deck, x of them will be black and y of them will be red, and x+y=26. As there are 26 of each color in the deck, then x+?=26 for the black cards in the deck and ?+y=26 for the red cards in the deck. As x+y=26 in the first randomly selected 26 cards, then the value of black cards in the other half of the deck must equal y, and the value of red cards in the other half of the deck must equal x meaning that "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."

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?

Answer:3 total, 2 sister and 1 brother Solution: Since the daughters in the family each have as many brothers as sisters the amount of sisters, with x standing for the amount of brothers, is x+1. As each brother has twice as many sisters as brothers, the amount of sisters must equal 2(x-1) or 2x-2. To find the number of brother: x+1=2x+1, 1=x-2, 3=x, which means that their are 3 brothers and 4 sisters (x+1= the number of sisters and x=3). This makes sense because a sister would have an equal amount of brothers to sisters, 3 sisters and 3 brothers, if there were 4 sisters and 3 brothers total, and each brother would have 4 sisters and 3 brothers, which is twice the amount of brothers to sisters.

17~21

Audrey Chen

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 read too low, since Dan is shown as 60kg and Sarah is 50kg, suppose 60+50=110, 105-110=-5, so that means the scale is smaller than 0 in the beginning

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?

If the total pennies is "x", Alice take 1/3x, so it has 2/3x left after Alice took it, than Bret take 1/3 out, after Alice took it, which is 2/3x*1/3= 2/9x, so in the beginning they have x, after Alice took it, it has 2/3x left, and Bret took 2/9x, so after Bret took it, it becomes 2/3x-2/9x= 4/9x-2/9x=2/9x left in the jar. Than Carla take 1/3 of the rest, so she took 1/3 of rest which is 2/9x*1/3=3/27x, so Alice took 1/3x, Bret tool 2/9x, Carla took 3/27x, three of them totaly took 1/3x+2/9x+3/27x=18/27x, so there still has x-18/27x= 9/27x= 1/3 left, 1/3x=40pennies, so x=120 pennies, so it was having 120 pennies in the jar.

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?

If we let total milk is x, total coffee is y. Than 1/4x+1/6y=8, and because every cup is 8ounce, x+y is multiple by 8. So make it easier, we use 1/4x+1/6y=8 * 12 to both sides. than we will got 3x+2y=96, now we have 3x+2y=96 and x+y is multiple of 8, and the number that multiple by 8 is 8, 16, 24, 32... so 2x+2y= 16, 32, 48, 64, 80, 96, since 3x+2y=96, it can't be more than 96. It will only have 6 possible number, so if you take 3x+2y=96 substracting 2x+2y=16, 32, 48, 64, 80, 96 you can get 6 possible x, which are 80, 64, 48, 32, 16, and 0. Than put the number into 3x+2y=96, if you put 80 in, will get 20, which is bigger than 8, and also 64, 48. If we use 32, it will equal to 8, but that means we have 0 coffee, but coffee can't be 0, so there's only 16 and 0 left. Since Angela had 1/4 of total amount of milk, milk can't be 0. So we got 16ounce than 16*(1/4)=4, so that means she had 8-4=4 's coffee. So 4=1/6 coffee, than the total amount of coffee would be 4*6=24. than x=16 and y=24, 16+24=40 40/8ounce=5, so at least have 5 cups of drinks, so that means at least they have 5 members in Angela's 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?

Since one clock runs 5 min faster per hour, the other is 5 min slower, after clock runs an hour, two clocks will have 10 min different from each other. 60 min an hour. 60/10=6, so after 6 hours two clocks will having one hour apart, and that would be 6AM.

21.Sven placed exactly in the middle among all runners in a race. Dan was slower than Sven, in 10th place, and Lars was in 16th place. How many runners were in the race?

There were 17 runners. Since lars was in 16th place, the runners at least have to be 16, than if Sven is placed exactly in the middle, it means it would have even number of runners. Because Dan is slower and he was at 10 place that tells us Seven has to be before 10th, and if there has 19 runners, Sven and Dan would be at the same place, so it should be 17 runners, than Sven would be at exactly in the middle which at 9th place.

22-25

Roland Will

22. During a vacation, it rained on 13 days, but when it rained in the morning, the afternoon was sunny, and every rainy afternoon was preceded by a sunny morning. There were 11 sunny mornings and 12 sunny afternoons. How long was the vacation?

Answer: 18 days of vacation.

Solution: 13 of the days of vacation were half sunny and half rainy. As there were 23 sunny mornings and afternoons (11 sunny mornings+12 sunny afternoons = 23 sunny mornings and afternoons), 13 of those sunny afternoons or mornings were on half rainy days. This means there are 10 sunny half-days left over, which equal 5 sunny full days. The 5 sunny full days plus the 13 half sunny/rainy days equal 18 total days of vacation.

23. Suppose you overhear the following conversation: Paul: How old are your three children? Paula: The product of their ages is 36 and the sum of their ages is the same as today's date. Paul: That is not enough information. Paula: The oldest child also has red hair. If you were Paul could you determine the ages of Paula's children? Explain.

Answer: If I were Paul this might be possible, but since we don’t know the date that Paula said this, it is not possible for us to find out.

Solution: There are many different combinations of three numbers that can be multiplied and will produce 36. As we do not know the date that Paula said this, the only thing we can be sure of is that the sum of the ages is less than 31 because no month has more than 31 days. Unfortunately, only one set of ages (ages 1 year old, 1 year old and 36 years old) has a sum greater than 31, which leaves many possible combinations open as possible. For today’s date, the 13th, ages of 2, 2, and 9 would produce 36 and have a sum of 13, but, again, it is uncertain. If it were the first of the month, there would be no possible combinations that would produce 36 and sum 1.

24. Two candles of equal length were lit at the same time. One candle took 6 hr to burn out and the other candle took 3 hr to burn out. After how much time was one candle exactly twice as long as the other candle?

Answer: 2 hours.

Solution: The faster burning candle took half the time to burn as the slower burning candle (3 hours/ 6 hours = 1/2), meaning it burned twice as fast. This means that after 2/3 of the total burning time for the faster burning candle it will be 1/3 of its original height and at the slower burning candle will be at 2/3 of its original height and 1/3 is half of 2/3. Since the faster burning candle took 3 hours to burn, 2/3 of its total burning time is 2 hours.

25. Two candles of length L and L + 1 were lit at 6:00 and 4:30, respectively. At 8:30 they had the same length. The longer candle died at 10:30 and the shorter candle died at 10:00. Find L.

Answer: L=2.

Solution: The shorter candle lasted for 4 hours and the longer candle lasted for 6 hours. As 6 hours – 4 hours = 2 hours and 2 hours / 4 hours = 1/2, the longer candle lasted 50% longer and was, therefore, 50% longer in length. This means that the +1 in L+1 on the longer candle was 1/2 of L. 1/2L=1, so L=2*1, L=2.

2. Bohao, Stewart, Dylan, Tim and Chan are the five players of a basketball team. Two are left handed and three right handed, Two are over 2m tall and three are under 2m, Bohao and Dylan are of the same handedness, whereas Tim and Chan use different hands. Stewart and Chan are of the same height range, while Dylan and Tim are in different height ranges. If you know that the one playing centre is over 2m tall and is left handed, can you guess his name?

-- If two are left handed and three and right handed then you know that Bohao and Dylan have to be right handed because they have to be of the same handedness and one of Tim and Chan have to be right handed, which accounts for the three right handed people. You still don't know which one of Tim or Chan is right handed. The question also states that Three people are under 2m and two are over two meters, if Stewart and Chan have to be of the same height, you know that they are both under 2m because one of Dylan or Tim have to be under two meters as well, which leaves the only person unaccounted for in the equation to be Tim. Because Tim is the only person left out of the equation you know that it must be Tim that is the centre over 2m, because it was either him or Chan who were right handed, and now you know that it is Chan who is right handed because Tim must satisfy the left handed criteria because he is over 2m tall. In the end you know the answer must be Tim.

2. Bohao, Stewart, Dylan, Tim and Chan are the five players of a basketball team. Two are left handed and three right handed, Two are over 2m tall and three are under 2m, Bohao and Dylan are of the same handedness, whereas Tim and Chan use different hands. Stewart and Chan are of the same height range, while Dylan and Tim are in different height ranges. If you know that the one playing centre is over 2m tall and is left handed, can you guess his name?

-- If two are left handed and three and right handed then you know that Bohao and Dylan have to be right handed because they have to be of the same handedness and one of Tim and Chan have to be right handed, which accounts for the three right handed people. You still don't know which one of Tim or Chan is right handed. The question also states that Three people are under 2m and two are over two meters, if Stewart and Chan have to be of the same height, you know that they are both under 2m because one of Dylan or Tim have to be under two meters as well, which leaves the only person unaccounted for in the equation to be Tim. Because Tim is the only person left out of the equation you know that it must be Tim that is the centre over 2m, because it was either him or Chan who were right handed, and now you know that it is Chan who is right handed because Tim must satisfy the left handed criteria because he is over 2m tall. In the end you know the answer must be Tim.

4.Six players - Petra, Carla, Janet, Sandra, Li and Fernanda - are competing in a chess tournament over a period of five days. Each player plays each of the others once. Three matches are played simultaneously during each of the five days. The first day, Carla beats Petra after 36 moves. The second day, Carla was again victorious when Janet failed to complete 40 moves within the required time limit. The third day had the most exciting match of all when Janet declared that she would checkmate Li in 8 moves and succeeded in doing so. On the fourth day, Petra defeated Sandra. Who played against Fernanda on the fifth day?

We know: first day Carla vs Petra, 2nd day Carla vs Janet, 3rd day Janet vs Li, 4th day Petra vs Sandra, 5th day ? vs Fernanda. so we have: 1st day, Sandra vs Janet, Li vs Fernanda 2nd day, Petra vs Li, Sandra vs Fernanda 3rd day, Petra vs Fernanda, Carla vs Sandra 4th day, Janet vs Fernanda, Caral vs Li so, on 5th day we find out that Petra vs Janet, Sandra vs Li, than we can figure Fernanda vs "Carla", so the answer is "carla".