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*System of equations AND Inequation* (Need help)

  1. Feb 8, 2008 #1
    [SOLVED] *System of equations AND Inequation* (Need help)...

    1. The problem statement, all variables and given/known data

    Alex is a professionel athlete. One day, he leaves for mountain hiking and ascends a coast to an average speed of 12 km/hour. On his way back, he borrows the same coast and descends to an average speed of 18 km/hour. The descent lasted 15 minutes less than the ascension.

    Find the coast length.

    P.S.: *Sorry for the typo, I had to translate this problem from french to english =.=....

    2. Relevant equations


    3. The attempt at a solution

    Where do I even start with this....
    This problem may be easy for some of you...well its a typical 9th grade question...

    (P.S.: I did attempt something..however I am not sure.Waiting for your answers/tips/advices...)
    Last edited: Feb 8, 2008
  2. jcsd
  3. Feb 8, 2008 #2
    umm, this problem comes from one of my math book chapter: System of Equations and Inequation
  4. Feb 8, 2008 #3


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    What's a 'coast'? No matter. Call it's length L. Then the first time is L/(12km/hr), and the second is L/(18km/hr). The difference of those two times is 15 min. Write an equation expressing that and solve for L.
  5. Feb 8, 2008 #4
    Since the speed is expressed in Km/hour...and if i convert this in km/minute...it would become:



    So the equation is...

    0.2m = 0.3m - 15????

    I solve this and find m...it still sounds weird...o.0
    Last edited: Feb 8, 2008
  6. Feb 8, 2008 #5
    how would the above formula(the 1 i just posted) can help find the length...

    is it normal that im facing(being a 9th grade student)difficulties in this problem,is it suppose to be an easy-level problem....?
  7. Feb 8, 2008 #6
    also,if i solve the above equation,it gives 150!!!! A guy siriously can not be hiking on a 150 KM track!!!! o.0...
  8. Feb 8, 2008 #7
  9. Feb 8, 2008 #8
    so,what do you think dick????
  10. Feb 8, 2008 #9


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    Ah, 'coast'='slope' or 'hill'. The equation becomes L/(0.2km/min)-L/(0.3km/min)=15min. The only unknown is L. Solve for it.
  11. Feb 8, 2008 #10

    D H

    Staff: Mentor

    It would help if you expressed units all the way through. If you had done this you would see that the equation is incorrect because the units don't match up. The '0.2' is more precisely stated as '0.2 km/minute', 'm' as 'm km', and 15 as '15 minutes'. (This makes your 'm' unitless -- just a number.) Being explicit,

    m*0.2 km^2/minute = m*0.3 km^2/minute - 15 minutes

    and this doesn't make a bit of sense, which is why your answer doesn't make a bit of sense. Re-read Dick's instructions.
  12. Feb 8, 2008 #11
    you equationd doesnt work.

    "The descent lasted 15 minutes less than the ascension"

    we dont even know how many minutes he took for the ascension....

    and we are looking for the length...ah i dont see where you're really getting...o.0
  13. Feb 8, 2008 #12
    um...0.2 kilometres/min doesnt seem wrong at all....in fact,its ok if i leave the unit as a KM rather transforming it into m...
  14. Feb 8, 2008 #13


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    You don't know the time for the ascent. But if the length is L, then that time can be written L/(0.2km/min). Time=distance/velocity.
  15. Feb 8, 2008 #14
    sorry if my reasonning seems mindless and newbish...=.=
  16. Feb 8, 2008 #15


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    There's nothing wrong with your reasoning so far. You just haven't finished. Read the advice you are getting carefully and think about it before posting again.
  17. Feb 8, 2008 #16

    L/(0.2km/m) - L(0.3km/m) = 15

    L/-0.1 = 15

    L = -1.5

    I messed this up..for sure
  18. Feb 8, 2008 #17


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    Sure did. Nothing wrong with the concept. Just bad algebra. L/0.2-L/0.3 is not L/(-0.1). You are subtracting fractions, you need to find a common denominator.
  19. Feb 8, 2008 #18
    HAHA,Sooorrrry it just came up in my mind,I rushed up with this...must pay attention next time.Thx


    L/(0.2Km/m) - L/(0.3km/m) = 15

    L/(0.6 km/m) - L/(0.6km/m) = 15

    0L = 9 KM???
    Last edited: Feb 8, 2008
  20. Feb 8, 2008 #19


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    You really need some practice. L/(0.2)=(3/3)*L/(0.2)=3L/(0.6). Multiply the second one by 2/2.
  21. Feb 8, 2008 #20
    L = 9km ?

    yup,i rushed up witht he above,forgot to multiply the L's...
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