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    Alice can complete a task in 18 days, and Bob can complete the same task in 24 days. If they work together, how long will it take for them to com
    Question

    Alice can complete a task in 18 days, and Bob can complete the same task in 24 days. If they work together, how long will it take for them to complete the task?

    A.

    1027 days 10\tfrac{2}{7} \text{ days} \quad​​

    B.

    8 days8 \text{ days} \quad​​

    C.

    10 days 10 \text{ days} \quad​​

    D.

    935 days 9\tfrac{3}{5} \text{ days}​​

    Correct option is A

    Given:

    Alice = 18 days, Bob = 24 days.

    Solution:
    Combined time T=1118+124.=\dfrac{1}{\dfrac{1}{18}+\dfrac{1}{24}}.​​

    T =1772.\dfrac{1}{\dfrac{7}{72}}.​​

    T=727=1027\dfrac{72}{7} =10\frac{2}{7}​ days

    Alternate Solution:
    Assume total work = LCM(18, 24) = 72 units.
    Alice’s rate =7218= \frac {72}{18}=​4 units/day; Bob’s rate =7224== \frac{72}{24}=​3 units/day.
    Together = 4+3=7 units/day

    Time =727=1027=\frac {72}7=10\frac{2}{7} days.

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