Exercise : Boat & Stream - General Questions
✔ Boat & Stream -
General Questions
21.
Speed of a boat in still water is 10 km/h. It goes 91 km downstream and returns. The time taken for the return journey is 6 hours more than the downstream journey. Find the speed of the stream.
View Answer
Answer: Option A
Explanation:
Explanation:
1. Let stream speed be \(s\). \(\frac{91}{10-s} - \frac{91}{10+s} = 6\).
2. \(91(10 + s - (10 - s)) = 6(100 - s^2)\).
3. \(182s = 600 - 6s^2 \implies 6s^2 + 182s - 600 = 0 \implies 3s^2 + 91s - 300 = 0\).
4. Solving the quadratic gives \(s = 3 \text{ km/h}\).
2. \(91(10 + s - (10 - s)) = 6(100 - s^2)\).
3. \(182s = 600 - 6s^2 \implies 6s^2 + 182s - 600 = 0 \implies 3s^2 + 91s - 300 = 0\).
4. Solving the quadratic gives \(s = 3 \text{ km/h}\).
22.
A man rows to a place 35 km in distance and back in 12 hours. He finds that he can row 5 km with the stream in the same time as 4 km against the stream. What is the speed of the boat in still water?
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Answer: Option A
Explanation:
Explanation:
1. Ratio of speeds \(D:U = 5:4\). Let speeds be \(5x\) and \(4x\).
2. Total time: \(\frac{35}{5x} + \frac{35}{4x} = 12 \implies \frac{7}{x} + \frac{8.75}{x} = 12\).
3. \(\frac{15.75}{x} = 12 \implies x = 1.3125\).
4. \(D = 6.5625\), \(U = 5.25\).
5. Still Water Speed = \(\frac{6.5625 + 5.25}{2} = 5.906 \text{ km/h}\).
2. Total time: \(\frac{35}{5x} + \frac{35}{4x} = 12 \implies \frac{7}{x} + \frac{8.75}{x} = 12\).
3. \(\frac{15.75}{x} = 12 \implies x = 1.3125\).
4. \(D = 6.5625\), \(U = 5.25\).
5. Still Water Speed = \(\frac{6.5625 + 5.25}{2} = 5.906 \text{ km/h}\).
23.
A boat takes 4 hours to travel from a point A to B downstream and back to A. If the speed of the boat in still water is 3 km/h and the stream is 1 km/h, find the distance AB.
View Answer
Answer: Option A
Explanation:
Explanation:
1. Downstream = \(3 + 1 = 4 \text{ km/h}\); Upstream = \(3 - 1 = 2 \text{ km/h}\).
2. \(\frac{D}{4} + \frac{D}{2} = 4 \implies \frac{3D}{4} = 4\).
3. \(D = 16 / 3 = 5.33 \text{ km}\).
2. \(\frac{D}{4} + \frac{D}{2} = 4 \implies \frac{3D}{4} = 4\).
3. \(D = 16 / 3 = 5.33 \text{ km}\).
24.
A swimmer's speed in still water is 5 km/h. He swims across a river 1 km wide. The river flows at 3 km/h. If he wants to reach the point directly opposite, what direction should he swim?
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Answer: Option A
Explanation:
Explanation:
1. To reach directly opposite, the swimmer's horizontal component must cancel the river's flow.
2. \(5 \times \sin(\theta) = 3 \implies \sin(\theta) = 0.6\).
3. \(\theta = \arcsin(0.6) \approx 36.87^\circ\).
4. Direction is 36.87° upstream from the perpendicular line.
2. \(5 \times \sin(\theta) = 3 \implies \sin(\theta) = 0.6\).
3. \(\theta = \arcsin(0.6) \approx 36.87^\circ\).
4. Direction is 36.87° upstream from the perpendicular line.
25.
The speed of a boat in still water is 5 km/h and the speed of the current is 3 km/h. If the boat takes 3 hours to go to a place and come back, the distance of the place is?
View Answer
Answer: Option A
Explanation:
Explanation:
1. Downstream speed = \(5 + 3 = 8 \text{ km/h}\); Upstream speed = \(5 - 3 = 2 \text{ km/h}\).
2. Equation: \(\frac{D}{8} + \frac{D}{2} = 3\).
3. \(\frac{D + 4D}{8} = 3 \implies \frac{5D}{8} = 3\).
4. \(5D = 24 \implies D = 4.8 \text{ km}\).
2. Equation: \(\frac{D}{8} + \frac{D}{2} = 3\).
3. \(\frac{D + 4D}{8} = 3 \implies \frac{5D}{8} = 3\).
4. \(5D = 24 \implies D = 4.8 \text{ km}\).