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Any mathematicians out there??

max888max888 Posts: 206
edited September 2010 in The bottom bracket
Does anybody want to have a crack at an algebraic puzzle, I have not got very far i.e. nowhere at all.

'A small swimming pool can be filled with two pipes in 3 hours. If the larger pipe alone takes 8 hours less than the smaller pipe to fill the pool, find the time in which it will be filled by each pipe singly.'

Thanks,

Max
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Posts

  • nolfnolf Posts: 2,016
    I'm struggling with that.

    Large pipe must be more than 3 hours, so small pipe must be more than 11.

    And I can't get further than that. :(
    "I hold it true, what'er befall;
    I feel it, when I sorrow most;
    'Tis better to have loved and lost;
    Than never to have loved at all."

    Alfred Tennyson
  • max888max888 Posts: 206
    Thanks for your help it's further than I got, I'll just keep going back to it.

    Max
  • nolfnolf Posts: 2,016
    Got it.

    PMed.
    "I hold it true, what'er befall;
    I feel it, when I sorrow most;
    'Tis better to have loved and lost;
    Than never to have loved at all."

    Alfred Tennyson
  • RichN95.RichN95. Posts: 24,649
    12 hours and 4 hours.

    Make the pool 300 units in size. Make the rates of the two pipes X and Y units per hour. (Y is the faster)

    Therefore 300/3=X+Y. So X=100-Y

    And 300/X - 8 = 300/Y

    Multiply by X and Y: 300Y -8XY= 300X

    Substitute X: 300Y -800Y +8Y^2 = 30,000 -300Y

    Simplify: Y^2 -25Y -3,750 = 0

    Solve : Y= 75 so X=25

    Therefore times are 300/75 and 300/25. 8 hours and 4 hours.
    Twitter: @RichN95
  • FlasheartFlasheart Posts: 1,278
    RichN95 wrote:
    12 hours and 4 hours.

    Make the pool 300 units in size. Make the rates of the two pipes X and Y units per hour. (Y is the faster)

    Therefore 300/3=X+Y. So X=100-Y

    And 300/X - 8 = 300/Y

    Multiply by X and Y: 300Y -8XY= 300X

    Substitute X: 300Y -800Y +8Y^2 = 30,000 -300Y

    Simplify: Y^2 -25Y -3,750 = 0

    Solve : Y= 75 so X=25

    Therefore times are 300/75 and 300/25. 8 hours and 4 hours.

    :shock: :shock: :? :? :oops: :oops:

    I is fick :oops:
    The universal aptitude for ineptitude makes any human accomplishment an incredible miracle. ...Stapp’s Ironical Paradox Law
    FCN3
    http://img87.yfrog.com/img87/336/mycubeb.jpg
    http://lonelymiddlesomethingguy.blogspot.com/
  • nolfnolf Posts: 2,016
    Same as I got, but different. I put pool full = 1 and solved it like:

    Pool Full = 1 (arbitrarily)

    large pipe time alone = x
    small pipe time alone = y,
    y = x+8

    3 hours is the total time so you divide it by the individual pipes to get their contribution.

    (3/x+8 ) + (3/x) = 1

    times by x(x+8 ) gives

    3x + 3(x+8 )l = x(x+8 )

    3x + 3x+24= x^2 + 8x
    (-6x, - 24) equals

    0 = x^2 + 8x - 6x - 24
    0 = x^2 + 2x - 24

    0 = (x-4)(x+6)

    only positive answer is that x (large pipe) = 4
    therefore y (small pipe) = x+8 = 12.
    "I hold it true, what'er befall;
    I feel it, when I sorrow most;
    'Tis better to have loved and lost;
    Than never to have loved at all."

    Alfred Tennyson
  • RichN95.RichN95. Posts: 24,649
    nolf wrote:
    Same as I got, but different. I put pool full = 1 and solved it like:

    The maths is essentially the same though.
    Twitter: @RichN95
  • softladsoftlad Posts: 3,587
    you lot need to get out more.... ;)
  • max888max888 Posts: 206
    Thanks everyone for your help, it's much appreciated! :)
  • mrushtonmrushton Posts: 5,182
    Good to know that 32 years after leaving school I am still 5H1T at algebra. X? Y? Why? I work at a Uni and sometimes I see equations on a board and the rabble studying them and think how smart they are. Recently had a Nuclear Technology Conference at the Uni and all of the Ph. D students were ridiculously smart. It prob.was akin to rocket science.
    M.Rushton
  • wheezeewheezee Posts: 461
    Did you lot just do Max's homework for him?
  • angry_birdangry_bird Posts: 3,784
    Umm i just sort of figured it straight away (without looking at the other answers) quite by accident i think, it sort of clicked :oops: I was always censored a algebra at school, i just didn't like the look of it... god knows what you guys have written up there but it just confuses me, thank god i decided not to bother studying physics at uni...
  • Flasheart wrote:
    RichN95 wrote:
    12 hours and 4 hours.

    Make the pool 300 units in size. Make the rates of the two pipes X and Y units per hour. (Y is the faster)

    Therefore 300/3=X+Y. So X=100-Y

    And 300/X - 8 = 300/Y

    Multiply by X and Y: 300Y -8XY= 300X

    Substitute X: 300Y -800Y +8Y^2 = 30,000 -300Y

    Simplify: Y^2 -25Y -3,750 = 0

    Solve : Y= 75 so X=25

    Therefore times are 300/75 and 300/25. 8 hours and 4 hours.

    :shock: :shock: :? :? :oops: :oops:

    I is fick :oops:
    i feel the same way!
    Coveryourcar.co.uk RT Tester
    north west of england.
  • nolfnolf Posts: 2,016
    Here's some more fun questions:

    Pool filled in 3 hours (originally), than a leak appeared!!

    If full, the pool completely empties in 5 hours through the annoying leak.

    How long does the pool take to fill, bearing in mind the annoying leak?
    "I hold it true, what'er befall;
    I feel it, when I sorrow most;
    'Tis better to have loved and lost;
    Than never to have loved at all."

    Alfred Tennyson
  • nolf wrote:
    Here's some more fun questions:

    Pool filled in 3 hours (originally), than a leak appeared!!

    If full, the pool completely empties in 5 hours through the annoying leak.

    How long does the pool take to fill, bearing in mind the annoying leak?
    9 hours

    Edit - no, 7.5 hours ...
  • max888max888 Posts: 206
    Did you lot just do Max's homework for him

    It's not technically homework, just a small pack to stop me forgetting everything over the holidays! :D
  • SplottboySplottboy Posts: 4,208
    Plug the hole or buy a new pool?!
  • garrynolangarrynolan Posts: 625
    Assume it fills at 100 gals per hour, pool holds 300 gals. 5 hours to empty = 300 divided by 5 = 60 gals per hour lost; ergo pools fills at 100 - 60 = 40 gals per hour. Filling 300 gal pool @ 40 gals per hour = 7hours 30mins. Don't ask me how to do this using 'proper' algebra as I wouldn't have a clue!
    By the way... can someone explain in layman's language how binary works? In 1st year at Secondary I was a lazy git so got kicked out of the top class into the next one down - they had already done binary, we hadn't, so I missed it. There was a question on my O-level paper using binary and I couldn't even attempt it. Ta.
    Visit Ireland - all of it! Cycle in Dublin and know fear!!
    exercise.png
  • RichN95.RichN95. Posts: 24,649
    Flasheart wrote:
    RichN95 wrote:
    12 hours and 4 hours.

    Make the pool 300 units in size. Make the rates of the two pipes X and Y units per hour. (Y is the faster)

    Therefore 300/3=X+Y. So X=100-Y

    And 300/X - 8 = 300/Y

    Multiply by X and Y: 300Y -8XY= 300X

    Substitute X: 300Y -800Y +8Y^2 = 30,000 -300Y

    Simplify: Y^2 -25Y -3,750 = 0

    Solve : Y= 75 so X=25

    Therefore times are 300/75 and 300/25. 8 hours and 4 hours.

    :shock: :shock: :? :? :oops: :oops:

    I is fick :oops:
    i feel the same way!

    We all show thickness in different ways. I didn't realise it was a bank holiday until they mentioned it on the radio at 8.30 on Monday morning. Now that's thick.
    Twitter: @RichN95
  • Weejie54Weejie54 Posts: 750
    What if it's raining?

    This looks interesting...
  • Oi!!!!!!!! VORDERMAN I said NOOOOOOOOOOOOOOOOOOO. :lol:
    Tail end Charlie

    The above post may contain traces of sarcasm or/and bullsh*t.
  • RichN95 wrote:
    Flasheart wrote:
    RichN95 wrote:
    12 hours and 4 hours.

    Make the pool 300 units in size. Make the rates of the two pipes X and Y units per hour. (Y is the faster)

    Therefore 300/3=X+Y. So X=100-Y

    And 300/X - 8 = 300/Y

    Multiply by X and Y: 300Y -8XY= 300X

    Substitute X: 300Y -800Y +8Y^2 = 30,000 -300Y

    Simplify: Y^2 -25Y -3,750 = 0

    Solve : Y= 75 so X=25

    Therefore times are 300/75 and 300/25. 8 hours and 4 hours.

    :shock: :shock: :? :? :oops: :oops:

    I is fick :oops:
    i feel the same way!

    We all show thickness in different ways. I didn't realise it was a bank holiday until they mentioned it on the radio at 8.30 on Monday morning. Now that's thick.
    no i think thats ignorance at it's best :lol::wink:
    Coveryourcar.co.uk RT Tester
    north west of england.
  • max888max888 Posts: 206
    no i think thats ignorance at it's best
    as they say "ignorance is bliss" :lol:
  • BunnehBunneh Posts: 1,329
    I'm terrible at mathematics but I'm exceptional at working with my hands (shut up Flasheart :lol: ). The first day at secondary school they gave us algebra, I'd never done it before and being the quiet lad I was back then I didn't ask. Spent my entire time at school struggling with maths with no one even helping me. The kids in the low sets were ignored and given up on, whilst the kids in high sets were encouraged.
  • max888max888 Posts: 206
    It not that like at my school. Last year I was in the second lowest set but got an A* at IGCSE. Everyone gets really good support and the teaching is excellent!
  • bompingtonbompington Posts: 7,674
    Max888 wrote:
    It not that like at my school. Last year I was in the second lowest set but got an A* at IGCSE. Everyone gets really good support and the teaching is excellent!
    @Max888's teacher - come on now, we all know it's easy to hack your kids' online accounts, but it's really unprofessional to use them!
  • max888max888 Posts: 206
    No hacking going on here but no censored , at my last school I could not do any maths at all but hey I just got top marks at GCSE, I ain't complaining.
  • BunnehBunneh Posts: 1,329
    Bear in mind my experiences are from the late 80s to early 90s. Thing have changed somewhat and I have done quite a good number of courses, from English through to my European Computer Driving License (chocolate teapot?). You get support, and good tutors who actually do give a damn - I seem to recall my Maths teacher giving up and my English teacher whining that my stories were too imaginative. I suspect she couldn't be arsed reading 12 pages...
  • beverickbeverick Posts: 3,461
    mrushton wrote:
    Good to know that 32 years after leaving school I am still 5H1T at algebra. X? Y? Why? I work at a Uni and sometimes I see equations on a board and the rabble studying them and think how smart they are. Recently had a Nuclear Technology Conference at the Uni and all of the Ph. D students were ridiculously smart. It prob.was akin to rocket science.

    Good to know that 31 years after leaving school, and having to learn sufficient algebra to pass various science exams, that I still don't understand it, I still can't do it and, what's more, during my entire working life I've never needed to.

    Bob
  • nolfnolf Posts: 2,016
    Turbo Man wrote:
    nolf wrote:
    Here's some more fun questions:

    Pool filled in 3 hours (originally), than a leak appeared!!

    If full, the pool completely empties in 5 hours through the annoying leak.

    How long does the pool take to fill, bearing in mind the annoying leak?
    9 hours

    Edit - no, 7.5 hours ...

    2nd one is right. :)
    "I hold it true, what'er befall;
    I feel it, when I sorrow most;
    'Tis better to have loved and lost;
    Than never to have loved at all."

    Alfred Tennyson
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