W.S 發問於 科學及數學數學 · 1 十年前

maths f.4 問題

maria takes 5 days more to do a job than John. Together, they can do the job in 6 days.How long does it take each to do the job alone??

ans: Maria: 15 days John: 10 days,,

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3 個解答

評分
  • 1 十年前
    最愛解答

    Let x be the days that John needs to do the job,

    then x + 5 is the day that Maria takes.

    From the given condition,

    6[1/x + 1/(x + 5)] = 1 ← (Since they need 6 days to work together to do the job.)

    6[(x + 5) + x]/x(x + 5) = 1

    6[(x + 5) + x]/x(x + 5) = 1

    12x + 30 = x2 + 5x

    x2 – 7x – 30 = 0

    (x - 10)(x + 3) = 0

    x = 10 or -3 (rejected)

    So, John takes 10 days to finish the job.

    Maria takes 15 days to finish the job.

    資料來源: Myself~~~
  • 1 十年前

    Let the time it takes Maria to do the job alone be x days and that of John be y days.

    x = y+ 5

    1/x + 1/y = 1/6

    Then 用代入法就計到答案la~

  • 1 十年前

    Let m and j be the number of days maria and john takes to do the job alone respectively

    since maria takes 5 days more to do a job than john,

    equation 1: m=j+5

    the proportion of job each of them can do in one day time is 1/m and 1/j respectively,

    thus they finished 1/6 of the work each day together

    therefore,

    equation 2: 1/m+1/j=1/6

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