ayun na nga ngayon lang ulit ako mag popost..

kayo mag post na kayo..

lapit na ang pasko!!!

pero bago mag pasko sana lahat tayo kasama sa fieldtrip..

masaya yun…

Boundaryless Organization

• a model that views organizations as having permeable boundaries. An organization has external boundaries that separate it from its suppliers and customers, and internal boundaries that provide demarcation to departments. This rigidity is removed in boundaryless organizations, where the goal is to develop greater flexibility and responsiveness to change and to facilitate the free exchange of information and ideas.

What would the Barbie Doll’s measurements be if she were life-size?
A: 39-21-33.

Who invented the coffee filter?
A: Melitta Bentz in Germany in 1908. To improve the the quality of coffee for her family, she pierced holes in a tin container, put a circular piece of absorbent paper in the bottom of it and put her creation over a coffee pot.

What essential piece of office equipment did Johnann Vaaler invent in 1900?
A: The paper Clip.

roblem 1: Two cars started from the same point, at 5 am, traveling in opposite directions at 40 and 50 mph respectively. At what time will they be 450 miles apart?

Solution to Problem 1:

• After t hours the distances D1 and D2, in miles per hour, traveled by the two cars are given by

  D1 = 40 t and D2 = 50 t

• After t hours the distance D separating the two cars is given by

  D = D1 + D2 = 40 t + 50 t = 90 t

• Distance D will be equal to 450 miles when

  D = 90 t = 450 miles

• To find the time t for D to be 450 miles, solve the above equation for t to obtain

  t = 5 hours.

  5 am + 5 hours = 10 am

Problem 2: At 9 am a car (A) began a journey from a point, traveling at 40 mph. At 10 am another car (B) started traveling from the same point at 60 mph in the same direction as car (A). At what time will car B pass car A?

Problem 3: Two trains, traveling towards each other, left from two stations that are 900 miles apart, at 4 pm. If the rate of the first train is 72 mph and the rate of the second train is 78 mph, at wthat time will they pass each other?

Solution to Problem 3:

• After t hours, the two trains will have traveled distances D1 and D2 (in miles) given by

  D1 = 72 t and D2 = 78 t

• After t hours total distance D traveled by the two trains is given by

  D = D1 + D2 = 72 t + 78 t = 150 t

• When distance D is equal to 900 miles, the two trains pass each other.

  150 t = 900

• Solve the above equation for t

  t = 6 hours.

Solution to Problem 2:

• After t hours the distances D1 traveled by car A is given by

  D1 = 40 t

• Car B starts at 10 am and will therefore have spent one hour less than car A when it passes it. After (t – 1) hours, distance D2 traveled by car B is given by

  D2 = 60 (t-1)

• When car B passes car A, they are at the same distance from the starting point and therefore D1 = D2 which gives

  40 t = 60 (t-1)

• Solve the above equation for t to find

  t = 3 hours

• Car B passes car A at

  9 + 3 = 12 pm

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• In three more years, Miguel’s grandfather will be six times as old as Miguel was last year. When Miguel’s present age is added to his grandfather’s present age, the total is 68. How old is each one now? Copyright © Elizabeth Stapel 1999-2009 All Rights Reserved

• g + 3 = 6(m – 1)
  m + g = 68
  g + 3 = 6(m – 1)
  g + 3 = 6m – 6
  g + 3 = 6(68 – g) – 6
  g + 3 = 408 – 6g – 6
  g + 3 = 402 – 6g
  g + 6g = 402 – 3
  7g = 399
  g = 57
  • One-half of Heather’s age two years from now plus one-third of her age three years ago is twenty years. How old is she now?
  • age now: H
    age two years from now: H + 2
    age three years ago: H – 3
    one-half of age two years from now: ( ¹/₂ )(H + 2) = ^H/₂ + 1
    one-third of age three years ago: ( ¹/₃ )(H – 3) = ^H/₃ – 1
    ^H/₂ + 1 + ^H/₃ – 1 = 20
    ^H/₂ + ^H/₃ = 20
    3H + 2H = 120
    5H = 120
    H = 24

  This problem refers to Heather’s age two years in the future and three years in the past. So I’ll pick a variable and label everything clearly:

  Now I need certain fractions of these ages:

  The sum of these two numbers is twenty, so I’ll add them and set this equal to 20:

  Heather is 24 years old.

  
  

This exercise refers not only to their present ages, but also to both their ages last year and their ages in three years, so labelling will be very important. I will label Miguel’s present age as “m” and his grandfather’s present age as “g“. Then m + g = 68. Miguel’s age “last year” was m – 1. His grandfather’s age “in three more years” will be g + 3. The grandfather’s “age three years from now” is six times Miguel’s “age last year” or, in math:

This gives me two equations with two variables:

Solving the first equation, I get m = 68 – g. (Note: It’s okay to solve for “g = 68 – m“, too. The problem will work out a bit differently in the middle, but the answer will be the same at the end.) I’ll plug “68 – g” into the second equation in place of “m“:

Since “g” stands for the grandfather’s current age, then the grandfather is 57 years old. Since m + g = 68, then m = 11, and Miguel is presently eleven years old.