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A team of 10 workers can complete a task in 24 days. How many days will 15 workers take to complete the same task?

Mathematics

ScanSolve AI Answer

Answer

Siku 16\text{Siku 16}

Step-by-step solution

4 steps

Huu ni mfano wa uwiano usio wa moja kwa moja (inverse proportion) kwa sababu idadi ya wafanyakazi inapoongezeka, idadi ya siku zinazohitajika kukamilisha kazi hupungua.

  1. Tambua uhusiano wa uwiano.

    Kwa uwiano usio wa moja kwa moja, bidhaa ya idadi ya wafanyakazi na idadi ya siku ni mara kwa mara.
    Hivyo, W1×D1=W2×D2W_1 \times D_1 = W_2 \times D_2, ambapo WW ni wafanyakazi na DD ni siku.

  2. Badilisha thamani zinazojulikana kwenye fomula.

    Tunajua:
    Wafanyakazi wa kwanza (W1W_1) = 10
    Siku za kwanza (D1D_1) = 24
    Wafanyakazi wapya (W2W_2) = 15
    Siku mpya (D2D_2) = xx

    10×24=15×x10 \times 24 = 15 \times x
  3. Rahisisha na tatua kwa xx.

    240=15x240 = 15x

    Ili kupata xx, gawanya pande zote mbili kwa 15:

    x=24015x = \frac{240}{15} x=16x = 16
  4. Toa jibu la mwisho.

    Hivyo, wafanyakazi 15 watachukua siku 16 kukamilisha kazi hiyo hiyo.

    Jibu la mwisho ni: Siku 16\text{Siku 16}

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