Question : A boar racer can row $21 \frac{3}{2}$ km/h in still water. If the speed of the river is 12.5 km/hr, it takes him 40 minutes to row to a place and back, how far off is the place (consider up to two decimals)?
Option 1: $5 \frac{5}{27}$ km
Option 2: $5 \frac{2}{5}$ km
Option 3: $4 \frac{5}{27}$ km
Option 4: $3 \frac{5}{27}$ km
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Correct Answer: $5 \frac{5}{27}$ km
Solution : A boat racer can row $21\frac{3}{2}$ km/h in still water. The speed of the river is 12.5 km/hr, it takes him 40 minutes to row to a place and back. Let the distance be $x$, then, Upstream speed = $21\frac{3}{2}$ km/h - 12.5 km/h = 22.5 - 12.5 = 10 km/h Downstream speed = 22.5 km/h + 12.5 km/h = 35 km/h According to the question, $\frac{x}{10} + \frac{x}{35} = \frac{40}{60}$ ⇒ $x(\frac{1}{10} + \frac{1}{35}) = \frac{2}{3}$ ⇒ $x(\frac{45}{350}) = \frac{2}{3}$ ⇒ $x = 2 × \frac{70}{3×9} $ ⇒ $x = 5\frac{5}{27}$ km Hence, The correct answer is $5\frac{5}{27}$ km.
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Question : The speed of a boat in still water is $5 \frac{1}{3} \mathrm{~km} / \mathrm{hr}$. It is found that the boat takes thrice as much time to row up as it does to row down the same distance in the river stream. Find the speed of the river stream.
Question : A man can row 10 km/hr in still water. When the river is running at a speed of 4.5 km/hr, then it takes him 2 hours to row to a place and comes back to the initial point. How far is the place (in km) (rounded off to two decimal places)?
Question : Rubi goes to a multiplex at a speed of 3 km/h to see a movie and reaches 5 minutes late. If she travels at the speed of 4 km/h she reaches 5 minutes early, then the distance of the multiplex from her starting point is:
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