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    Manyata rowed a certain distance downstream in 2 hours while it took her 30 minutes more to row the same distance upstream. How much time will she tak
    Question

    Manyata rowed a certain distance downstream in 2 hours while it took her 30 minutes more to row the same distance upstream. How much time will she take to make the two-way journey in still water?

    A.

    4:15:10 hours

    B.

    4:10 hours

    C.

    4:26:40 hours

    D.

    4:02:20 hours

    Correct option is C

    Manyata rowed a certain distance downstream in 2 hours while it took her 30 minutes more to row the same distance upstream. How much time will she take to make the two-way journey in still water?

    Given:

    - Time downstream (td)(t_d)​ = 2 hours

    - Time upstream (tu)(t_u) ​= 2 hours + 30 minutes = 2.5 hours

    - Distance downstream = Distance upstream = d

    Speeds downstream and upstream

    Speed downstream, Sd=d2S_d = \frac{d }{2}​​

    Speed upstream, Su=d2.5=2d5S_u =\frac{ d }{ 2.5} = \frac{2d }{ 5}​​

    Calculate speed in still water (S)

    S=Sd+Su2=d2+2d52=5d10+4d102=9d102=9d20S = \frac{S_d + S_u}{2} = \frac{\frac{d}{2} + \frac{2d}{5}}{2} = \frac{\frac{5d}{10} + \frac{4d}{10}}{2} = \frac{\frac{9d}{10}}{2} = \frac{9d}{20}​​

    Calculate time taken for two-way journey

    Total distance = 2d

    Time = Time=Total distanceSpeed in still water=2d9d20=2d×209d=409 hours\text{Time} = \frac{\text{Total distance}}{\text{Speed in still water}} = \frac{2d}{\frac{9d}{20}} = 2d \times \frac{20}{9d} = \frac{40}{9} \text{ hours}​​

    Convert time to hours, minutes, and seconds

    409\frac{40}{9}​ ≈ 4.4444 hours = 4 hours + 0.4444 × 60 minutes = 4 hours 26 minutes + 0.67 × 60 seconds ≈ 40 seconds

    Time taken for two-way journey = 4 hours 26 minutes 40 seconds

    Option (C) 4:26:40 hours

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