Question : A man rows a boat a certain distance downstream in 9 hours, while it takes 18 hours to row the same distance upstream. How many hours will it take him to row three-fifths of the same distance in still water?
Option 1: 9.5
Option 2: 7.2
Option 3: 10
Option 4: 12
Correct Answer: 7.2
Solution :
Given: Time taken for upstream = 18 hours
Time taken for downstream = 9 hours
LCM of 9 and 18 is 18.
Let the distance be 18 km.
Downstream speed = $\frac{\text{Distance}}{\text{Time}}$ = $\frac{18}{9}$ = 2 km/hr
Upstream speed = $\frac{18}{18}$ = 1 km/hr
Speed of the boat in still water = $\frac{1+2}{2}$ = $\frac{3}{2}$ = 1.5 km/hr
Now, $\frac{3}{5}$th of 18 km = $\frac{3}{5}\times 18$ = $\frac{54}{5}$ km
Thus, the boat can row $\frac{54}{5}$ km with a speed of 1.5 km/hr = $\frac{\frac{54}{5}}{1.5}$ = $\frac{54}{7.5}$ = 7.2 hours
Hence, the correct answer is 7.2.
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