Question : A boat can cover 120 km upstream and back in a total of 30 hours, and 25 km upstream and 40 km downstream in a total of 7 hours. How much distance will the boat cover in 16 hours in still water?
Option 1: 200 km
Option 2: 180 km
Option 3: 175 km
Option 4: 225 km
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Correct Answer: 200 km
Solution : Let the speed of the boat in still water be $x$ km/hr and the speed of the current be $y$ km/hr. Speed downstream = $x + y$ Speed upstream = $x - y$ Now, $\text{Time} = \frac{\text{Distance}}{\text{Speed}}$ $\frac{120}{x + y} + \frac{120}{x - y} = 30$....(1) and$\frac{40}{x + y} + \frac{25}{x – y} = 7$ ....(2) Multiplying equation (2) by 3, we get, $\frac{120}{x + y} + \frac{75}{x – y} = 21$ ......(3) Subtracting equation (3) from (1), we get, $\frac{45}{x – y} = 9$ $⇒x - y = 5$.......(4) Putting the value of $x - y$ in equation (2), we get, $x + y = 20$ .......(5) Solving these two equations, we get the values of $x$ and $y$. $x = 12.5$ and $y = 7.5$ Distance covered by the boat in 16 hours in still water = 16 × 12.5 = 200 km Hence, the correct answer is 200 km.
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Question : A boat covers a distance of 80 km downstream in 8 hours, while it takes 10 hours to cover the same distance upstream. What is the speed (in km/hr) of the boat in still water?
Question : A boat goes 20 km upstream and 44 km downstream in 8 hours. In 5 hours, it goes 15 km upstream and 22 km downstream. Determine the speed of the boat in still water.
Question : A boat goes 4 km upstream and 4 km downstream in an hour. The same boat goes 5 km downstream and 3 km upstream in 55 minutes. What is the speed (in km/hr) of the boat in still water?
Question : A boat moves 25 km upstream and 39 km downstream in 8 hours. It travels 35 km upstream and 52 km downstream in 11 hours. What is the speed of the stream if it travels at a uniform speed?
Question : A boat can go 5 km upstream and $7 \frac{1}{2}$ km downstream in 45 minutes. It can also go 5 km downstream and 2.5 km upstream in 25 minutes. How much time (in minutes) will it take to go 6 km upstream?
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