Question : The speed of a boat in standing water is 6 km/hr and the speed of the stream is 2.5 km/hr. A man rows to a place at a distance of 59.5 kilometres and comes back to the starting point. The total time taken by him is:
Option 1: 16 hours
Option 2: 24 hours
Option 3: 22 hours
Option 4: 18 hours
Correct Answer: 24 hours
Solution :
The total time taken by the man can be calculated by adding the time taken to row downstream (with the current) and the time taken to row upstream (against the current).
The effective speed of the boat while going downstream (with the current) is the sum of the speed of the boat in still water and the speed of the stream. So, it's 6 + 2.5 = 8.5 km/hr
The effective speed of the boat while going upstream (against the current) is the difference between the speed of the boat in still water and the speed of the stream. So, it's 6 – 2.5 = 3.5 km/hr
$\text{Time} = \frac{\text{Distance}}{\text{Speed}}$
So, the total time taken by the man to row to a place and come back is:
$\text{Time total} = \frac{\text{Distance}_{\text{downstream}}}{\text{Speed}_{\text{downstream}}} + \frac{\text{Distance}_{\text{upstream}}}{\text{Speed}_{\text{upstream}}} $
$= \frac{59.5}{8.5} + \frac{59.5}{3.5}$
$ = \frac{\frac{119}{2}}{\frac{17}{2}} + \frac{\frac{119}{2}}{\frac{7}{2}}$
$= \frac{119}{17} + \frac{119}{7}$
$= 7 + 17$
$= 24$
Hence, the correct answer is 24 hours.
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