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Practice — 45 people can finish a project in 15 days. For the same workload, 15 people are used. All people have equal productivity. In how many days can this project be completed?

Mathematics

ScanSolve AI Answer

Answer

45 days\text{45 days}

Step-by-step solution

4 steps

Hili ni tatizo la uwiano usio wa moja kwa moja. Idadi ya watu na idadi ya siku zinazohitajika kumaliza kazi ni kinyume.

  1. Tambua maadili uliyopewa.

    Tuna idadi ya awali ya watu (P1P_1) na siku (D1D_1), na idadi mpya ya watu (P2P_2). Tunahitaji kupata idadi mpya ya siku (D2D_2).
    P1=45P_1 = 45 watu
    D1=15D_1 = 15 siku
    P2=15P_2 = 15 watu
    D2=?D_2 = ? siku

  2. Tumia fomula ya uwiano usio wa moja kwa moja.

    Kwa uwiano usio wa moja kwa moja, bidhaa ya idadi ya watu na siku inabaki sawa:

    P1×D1=P2×D2P_1 \times D_1 = P_2 \times D_2
  3. Badilisha maadili kwenye fomula.

    45×15=15×D245 \times 15 = 15 \times D_2
  4. Tatua kwa D2D_2.

    Kwanza, zidisha upande wa kushoto:

    675=15×D2675 = 15 \times D_2

    Sasa, gawanya pande zote mbili kwa 15 ili kupata D2D_2:

    D2=67515D_2 = \frac{675}{15} D2=45D_2 = 45

    Hivyo, mradi utakamilika kwa siku 45.

    Jibu sahihi ni 45 days.
    45 days\text{45 days}

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