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?

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 $$(t_d)$$​ = 2 hours

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

- Distance downstream = Distance upstream = d

Speeds downstream and upstream

Speed downstream, $$S_d = \frac{d }{2}$$​​

Speed upstream, $$S_u =\frac{ d }{ 2.5} = \frac{2d }{ 5}$$​​

Calculate speed in still water (S)

​$$S = \frac{S_d + S_u}{2} = \frac{\frac{d}{2} + \frac{2d}{5}}{2} = \frac{\frac{5d}{10} + \frac{4d}{10}}{2} = \frac{\frac{9d}{10}}{2} = \frac{9d}{20}$$​​

Calculate time taken for two-way journey

Total distance = 2d

Time = $$\text{Time} = \frac{\text{Total distance}}{\text{Speed in still water}} = \frac{2d}{\frac{9d}{20}} = 2d \times \frac{20}{9d} = \frac{40}{9} \text{ hours}$$​​

Convert time to hours, minutes, and seconds

$$\frac{40}{9}$$​ ≈ 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