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Algebra - Who's the Lazy Bugger?

(34)
Posted at 10:19 am by Miss Loi in E-Maths Questions

As Miss Loi embarks on yet another epic weekend of endless joss sticks sessions, here’s a short and simple and innocent-looking E-Maths problem which had many of her students stumped *scratches head* for you to ponder upon:

Two students Bryan and Joan can complete a science project in 10 hours. If Bryan alone can complete the science project in 15 hours, how long will Joan take to complete the science project by herself?

P.S. This is a serious question ok??? Definitely NOT an April’s Fool joke!

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Comments & Reactions

34 Comments



  1. 2007
    Apr
    3
    Tue
    8:06am
     
    1

    Joan takes 30 hours. :D



  2. 2007
    Apr
    3
    Tue
    12:10pm
     
    2

    James where's your working?!

    Minus marks!!!



  3. 2007
    Apr
    3
    Tue
    4:07pm
     
    3

    alamak, gif question on April Fools' Day! Sure treat it as joke wan mah!

    Nobody dare to answer on tat day, scared answer oredi got bombed. Today answer aso bombed. walau! hahaha.......



  4. 2007
    Apr
    3
    Tue
    4:38pm
     
    4

    oh, soli... soli... miss loi,
    I said the b*** word twice. Pleeeease dun report me to the police.

    Read this.
    http://spawnily.livejournal.com/413020.html

  5. Kiroii's Avatar
    Kiroii says


    2007
    Apr
    27
    Fri
    1:31am
     
    5

    let joan's total time alone be x

    1/15 + 1/x = 1/10
    10x + 150 = 15x (using cross multiply)
    150= 5x
    x=30
    joan requires 30 hrs



  6. 2007
    Apr
    27
    Fri
    11:27am
     
    6

    Thanx for the workings, Kiroii.

    In your haste (perhaps to impress Miss Loi haha), you didn't put in the plus signs!

    For these kind of questions, Miss Loi always tell her students to look at it the other way round:

    In ONE hour, assuming constant workrate

    • Bryan does 1/15 parts of the total work for 1 hour.
    • Joan does 1/x parts of the total work for 1 hour.
    • Total work done in 1 hour is 1/10 = sum of Bryan and Joan's efforts for this 1 hour = to your equation above!

    P.S. But in reality most people don't work like this coz we are not robots!

  7. ashton's Avatar
    ashton says


    2008
    Sep
    11
    Thu
    5:56pm
     
    7

    aiyoh..just came across this. Isn't it simpler by just mulitplying to get 3 projects which the two of them will then take 30 hours. Since Bryan will take 15 hours per project, so in 30 hours he will finish 2, thus Joan will take 30 hours to finish that one project.... simple, right? no need for algebra, lazy or otherwise.



  8. 2008
    Sep
    13
    Sat
    1:20pm
     
    8

    Welcome to Jφss Sticks Ashton and thanks for contributing your Heuristic Approach (if Miss Loi may humbly use this word in a sense - though she prefers to call this common sense).

    What Ashton said is essentially this:

    ***

    Given that in 10 hours:
    Brian + Joan does 1 x project in 10 hrs.

    So in 30 hours:

    • Brian + Joan can do a total of 3 x projects.
    • But Brian alone does 2 x projects (since he can do 1 project in 15 hours)
      ⇒ Joane does the remaining 3-2 = 1 project in this 30 hrs
      ⇒ Joane alone takes 30 hrs to complete 1 project.

    ***

    So to use this approach for this question, the onus is on the student to first:

    Multiply Brian+Joan's hours (10 hrs) by a factor to make them > Brian's hour alone (i.e. 15 hours)
    *multiplying by 3 in this case gives nice whole numbers to work with

    However, this is something that weaker students (esp sec sch students who're suffering from the algebra mindset addiction syndrome in exam conditions) might not be able to see.

    So some may find the

    1/(Brian's hrs) + 1/(Joan's hrs) = 1/(Brian + Joan's hrs)

    described here a more convenient 'formula', which incidentally, can still be used if the question has been changed to "Given that Jane takes 15 hours more than Brian to complete the project on her own ... ".

    But ultimately, there's often more than one way to solve math problems, and it's nice to be able to highlight and discuss this in the comments box (which is the main purpose of this blog afterall), and at the end of the day students should follow whichever method that they are most comfortable with.

  9. ashton's Avatar
    ashton says


    2008
    Sep
    13
    Sat
    2:40pm
     
    9

    Hi Miss Loi

    I came across this page because I was reading about your "PSLE 1 Higher Education 0", of how PSLE maths questions seem to mirror those you are teaching at O and A levels. Fyi, this Brian & Jones type of question is commonly asked in PSLE and Primary School Maths Olympiad too..hehe, and students are taught using the lowest common factor to work out the solution.



  10. 2008
    Sep
    14
    Sun
    9:09am
     
    10

    Yeap, knew you were coming from PSLE perspective upon seeing your method ;) Are you a primary school cher?

    It's amazing how many kids 'unlearn' the stuffs they've been taught in primary school (when algebra seems to be a taboo) once they're in secondary school. There must be a missing link somewhere.

    Oh well ...

  11. 7inx's Avatar
    7inx says


    2008
    Sep
    14
    Sun
    9:36am
     
    11

    i m from malaysia,secondary school 3rd years(form 3), what gred tis question belongs?
    can i ask about tis question? i dun understand about tis question n the equation too.

  12. ashton's Avatar
    ashton says


    2008
    Sep
    14
    Sun
    4:34pm
     
    12

    No lah...just a dad (with a psle-year boy and two younger ones) aspiring to be a super tutor. $20k or more - that's inspiring. Can qualify or not? My boy got lots of Maths Olympiad awards. Hey...how about a joint venture? Then we would have covered all grounds, from P1 to Sec 4...hehe.



  13. 2008
    Sep
    15
    Mon
    2:52pm
     
    13

    Selamat Datang ke Jφss Sticks 7inx! Have you read through comment #6 and reference the equation in comment #5? Do email Miss Loi directly if you're still not clear about this.

    Ashton: Sigh ... 20k seems to be the notorious figure in the tuition trade these days. For the record, Miss Loi most certainly didn't utter that magic number so your inspiration may have been misplaced.

  14. ashton's Avatar
    ashton says


    2008
    Sep
    15
    Mon
    4:27pm
     
    14

    Aiyah, miss loi, you are just being humble. We all know temples are very rich one (it was reported in the papers in case you didn't know).

    Btw, I always love to ask this question to all aspiring Maths tutors and established ones. Care to solve it?

    Pat is twice as old as Chris was when Pat was as old as Chris is now.
    If Pat is 24 now, how old is Chris now?

    If this is too chicken feed for you, give it to your students and see how many can solve it...hehe...

  15. JH's Avatar
    JH says


    2008
    Sep
    16
    Tue
    3:17pm
     
    15

    O_O ashton thats like an IQ question... for me its not enough infomation... lol

  16. ashton's Avatar
    ashton says


    2008
    Sep
    16
    Tue
    3:33pm
     
    16

    Fail! :) The info is all there.

    1st info: Pat is twice as old as when Chris was
    2nd info: Pat is 24 years old now
    3rd info: Chris was 12 years old then...
    .....can solve? haha.

    Since we are on the algebra page and for the lazy ones, based on the above 3 info, here goes:

    PN = 2 CT (PN is of course Pat Now and CT is Chris Then)
    PN = 24
    CT = 12
    .........
    one more clue... PT = CN
    another clue...PN - PT = ?

  17. WS's Avatar
    WS says


    2008
    Sep
    16
    Tue
    6:07pm
     
    17

    PN = 24, CT = 12, PT = CN = 18

  18. ashton's Avatar
    ashton says


    2008
    Sep
    16
    Tue
    6:14pm
     
    18

    WS

    Like Ms Loi always says (from what i have read)...show your workings! hehe..I am getting the hang of being a tutor.

    PN - PT = CN - CT
    24 - CN = CN - 12
    36 = 2 CN
    CN = 18

    ....there you go.



  19. 2008
    Sep
    16
    Tue
    10:57pm
     
    19

    Aiyoh Ashton you seem to have brought your band of brothers here in Miss Loi's absence - and you've presented the solution before The Order of The Temple has the chance to answer!

    Anyways, your question did cause some headache stir amongst several members at The Temple but since the solution is out, Miss Loi shall just put up The Temple's way of solving this which may hopefully help all visualize things:

    The key lies in how we extract info from the dizzying sentence in the question and organize them into the two timelines via the keywords "was" and "is" i.e.

    1. Chris IS X now. (that's what we're trying to find)
    2. Pat WAS as old as Chris IS now ⇒ Pat WAS X.
    3. Pat IS 24.
    4. Pat IS twice as old as Chris WAS ⇒ Chris WAS 12.

    Filling up the table:

    WAS IS
    Pat X 24
    Chris 12 X

    We can then clearly see that:
    24 - X = X - 12 ⇒ X = 18 ;)

  20. ashton's Avatar
    ashton says


    2008
    Sep
    17
    Wed
    10:43am
     
    20

    Bravo, Miss Loi! So illuminating (must be the full moon effect).

    Well, this gets me into the mood...

    "The key lies in how we extract info..." Below is another question (this was asked during P4 maths lesson) that requires you to really know how to extract the info to solve.

    Postman: How are your 3 daughters, Mr Lim?
    Mr Lim: They are fine. Thank you.
    Postman: How old are they now?
    Mr Lim: The product of their 3 ages is 36. The sum of their ages is the same as my house number.
    Postman: Err.. I can't figure it out.
    Mr LIm: Well, my eldest daughter is waiting for her letter now.
    Postman: Oh, I got it. Thanks

    Can you get it? :)

  21. kiddo's Avatar
    kiddo says


    2008
    Sep
    17
    Wed
    11:08pm
     
    21

    Answering in absence of members of the Temple...shh

    'The product of their 3 ages is 36.'
    That's the only relevant statement to the postman's query.
    Unique expression of 36 as a product of 3 DIFFERENT factors is 36 = 2 x 3 x 6
    & these 3 factors are the ages of Mr Lim's daughters.

  22. ashton's Avatar
    ashton says


    2008
    Sep
    18
    Thu
    9:37am
     
    22

    Ah kiddo, nice try.

    But you didn't take into consideration the sum of their ages and that the postman would jolly well know the house number. So if it's 2, 3 & 6, the sum would be 11 (which would then be the house number) but the postman said he could not figure it out...

  23. kiddo's Avatar
    kiddo says


    2008
    Sep
    18
    Thu
    10:51am
     
    23

    What? Mr Lim's other statements are also relevant?

    Well I forgot that 1 is a factor of every number.
    So as product of different factors,
    36 = 1 x 2 x 18
    = 1 x 3 x 12
    = 1 x 4 x 9
    So these other factors may well be ages of 3 daughters too.

    But just can't figure out how 'my eldest daughter is waiting for her letter now' ties in. Any more hints, ashton?

  24. ashton's Avatar
    ashton says


    2008
    Sep
    18
    Thu
    11:33am
     
    24

    You are almost there...

    In Primary school (which like Miss Loi mentioned earlier, many who have graduated to Secondary have unlearned what was taught before), there is this method called "Guess and check".

    Hint: The Postman knows the house number, yet he was stumped to come up with their ages till Mr Lim's last reply.

  25. kiddo's Avatar
    kiddo says


    2008
    Sep
    18
    Thu
    1:55pm
     
    25

    We deduce house number is not 11 (= 2 + 3 + 6),
    14 (= 1 + 4 + 9), 16 (= 1 + 3 + 12) or 21 (= 1 + 2 + 18)
    but does that help?

    The last reply that enlightened the postman is the statement that stumps me. What's the link between the eldest daughter's 'age' & 'letter'?

  26. ashton's Avatar
    ashton says


    2008
    Sep
    18
    Thu
    2:22pm
     
    26

    Why don't you list down all the possible combinations?

    Product Sum
    1 1 36 = 38
    1 2 18 = 21
    1 3 12 = 16
    1 4 9 = 14
    1 6 6 = 13
    2 2 9 = 13
    2 3 6 = 11
    3 3 4 = 10

    Can you see something there?

  27. kiddo's Avatar
    kiddo says


    2008
    Sep
    18
    Thu
    2:58pm
     
    27

    Thanks Ashton. Are their ages are 2, 2 and 9?

  28. ashton's Avatar
    ashton says


    2008
    Sep
    18
    Thu
    3:21pm
     
    28

    Clap! Clap!



  29. 2008
    Sep
    19
    Fri
    1:22am
     
    29

    On behalf of The Temple, Miss Loi would like to thank you Ashton for making her miss her Channel 55/255 TVB drama just now :P

    This is exactly the sort of question which a P4 kid will answer with ease but on the other hand will leave an adult hopelessly stumped.

    In any case, probably being a P4 kid at heart, Miss Loi believes she has the full answer and explanation (and just to prove that she really does know: you'll just have to imagine you're the postman who's supposed to know it all - right? RIGHT? ;) ) but she shan't reveal it now coz she would like to pose this question to others in the meantime :D

    Wow the answer really JUMPED right out from the screen! Hahaha ...

  30. ashton's Avatar
    ashton says


    2008
    Sep
    19
    Fri
    5:43pm
     
    30

    Well Miss Loi, while you and your devotees are having fun with this P4 question, let me pose just one more. So that those who are really keen, can have more fun over the weekend. (evil laugh....)

    Four friends need to cross a bridge.
    They start on the same side of the bridge.
    A maximum of two people can cross at any time.
    It is night and they have just one lamp.
    People that cross the bridge must carry the lamp to see the way.
    A pair must walk together at the rate of the slower person:

    * Rachel: - takes 1 minute to cross

    * Ben: - takes 2 minutes to cross

    * George: - takes 7 minutes to cross

    * Yvonne: - takes 10 minutes to cross

    The second fastest solution gets the friends across in 21 minutes.
    The fastest solution takes 17 minutes. Can you work out how it is done? :)



  31. 2008
    Sep
    19
    Fri
    10:28pm
     
    31

    I got the ans for the above qn liao... solved in 5 mins....

    the 2nd faster solution:
    Yvonne + Rachel = From A (Starting pt) to B (Ending pt). 10 mins
    Rachel = From B to A. 1 min
    George + Rachel = From A to B. 7 mins
    Rachel = From B to A. 1 min
    Ben + Rachel = From A to B. 2 mins
    Total time spent= 10 + 1 + 7 + 1 + 2 = 21 mins

    Fastest solution:
    Ben + Rachel = From A to B. 2 mins
    Rachel = From B to A. 1 min
    Yvonne + George = From A to B. 10 mins
    Ben = From B to A. 2 mins
    Ben + Rachel = From A to B. 2 mins
    Total time = 2 + 1 + 10 + 2 + 2 = 17 mins.

    Tada!

  32. miy0k0's Avatar
    miy0k0 says


    2008
    Sep
    21
    Sun
    8:28am
     
    32

    are those PSLE questions?erm...i dun understand the question Postman: How are your 3 daughters, Mr Lim?
    Mr Lim: They are fine. Thank you.
    Postman: How old are they now?
    Mr Lim: The product of their 3 ages is 36. The sum of their ages is the same as my house number.
    Postman: Err.. I can’t figure it out.
    Mr LIm: Well, my eldest daughter is waiting for her letter now.
    Postman: Oh, I got it. Thanks

  33. Smiley:)'s Avatar
    Smiley:) says


    2009
    Feb
    13
    Fri
    11:03pm
     
    33

    I don't understand why 24- x= x-12 then how to get 36?



  34. 2009
    Feb
    28
    Sat
    11:37am
     
    34

    Simplify the problem. Look from doing 2 set of project instead.

    1 project for B and J = 10 hrs
    2 projects for B and J = 20 hrs

    if 1 project for B = 15 hrs
    then 1 project for J = 20 - 15 = 5 hrs.

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