Exercise : Boat & Stream - General Questions
✔ Boat & Stream -
General Questions
1.
A boat travels at 12 km/h in still water. The speed of the stream is 3 km/h. Find the speed of the boat downstream and upstream.
View Answer
Answer: Option A
Explanation:
Explanation:
1. Speed Downstream is calculated by adding the speed of the boat in still water and the speed of the stream: \(V_{down} = V_{boat} + V_{stream}\).
2. \(V_{down} = 12 + 3 = 15 \text{ km/h}\).
3. Speed Upstream is calculated by subtracting the speed of the stream from the speed of the boat in still water: \(V_{up} = V_{boat} - V_{stream}\).
4. \(V_{up} = 12 - 3 = 9 \text{ km/h}\).
2. \(V_{down} = 12 + 3 = 15 \text{ km/h}\).
3. Speed Upstream is calculated by subtracting the speed of the stream from the speed of the boat in still water: \(V_{up} = V_{boat} - V_{stream}\).
4. \(V_{up} = 12 - 3 = 9 \text{ km/h}\).
2.
A man can row downstream at 18 km/h and upstream at 10 km/h. Find the speed of the man in still water.
View Answer
Answer: Option A
Explanation:
Explanation:
1. The formula for the speed of a boat (or man) in still water is the average of the downstream and upstream speeds.
2. \(\text{Speed in still water} = \frac{\text{Downstream Speed} + \text{Upstream Speed}}{2}\).
3. \(\text{Speed in still water} = \frac{18 + 10}{2} = \frac{28}{2} = 14 \text{ km/h}\).
2. \(\text{Speed in still water} = \frac{\text{Downstream Speed} + \text{Upstream Speed}}{2}\).
3. \(\text{Speed in still water} = \frac{18 + 10}{2} = \frac{28}{2} = 14 \text{ km/h}\).
3.
The speed of a boat downstream is 20 km/h and the speed of the stream is 4 km/h. Find the speed of the boat upstream.
View Answer
Answer: Option A
Explanation:
Explanation:
1. First, find the speed of the boat in still water: \(V_{still} = V_{down} - V_{stream} = 20 - 4 = 16 \text{ km/h}\).
2. Now, find the upstream speed: \(V_{up} = V_{still} - V_{stream}\).
3. \(V_{up} = 16 - 4 = 12 \text{ km/h}\).
2. Now, find the upstream speed: \(V_{up} = V_{still} - V_{stream}\).
3. \(V_{up} = 16 - 4 = 12 \text{ km/h}\).
4.
A boat covers 32 km downstream in 4 hours. Find the speed of the boat downstream.
View Answer
Answer: Option A
Explanation:
Explanation:
1. Speed is defined as the distance traveled per unit of time: \(\text{Speed} = \frac{\text{Distance}}{\text{Time}}\).
2. \(\text{Downstream Speed} = \frac{32 \text{ km}}{4 \text{ hours}} = 8 \text{ km/h}\).
2. \(\text{Downstream Speed} = \frac{32 \text{ km}}{4 \text{ hours}} = 8 \text{ km/h}\).
5.
A man rows 15 km upstream in 3 hours. If the speed of the stream is 2 km/h, find his speed in still water.
View Answer
Answer: Option A
Explanation:
Explanation:
1. First, calculate the upstream speed: \(V_{up} = \frac{15}{3} = 5 \text{ km/h}\).
2. The speed in still water is the sum of the upstream speed and the stream speed: \(V_{still} = V_{up} + V_{stream}\).
3. \(V_{still} = 5 + 2 = 7 \text{ km/h}\).
2. The speed in still water is the sum of the upstream speed and the stream speed: \(V_{still} = V_{up} + V_{stream}\).
3. \(V_{still} = 5 + 2 = 7 \text{ km/h}\).
6.
A boat goes 24 km upstream and 28 km downstream in 6 hours. If the speed of the boat in still water is 10 km/h, find the speed of the stream.
View Answer
Answer: Option A
Explanation:
Explanation:
1. Let the speed of the stream be \(x \text{ km/h}\).
2. Upstream speed = \(10 - x\); Downstream speed = \(10 + x\).
3. Total time equation: \(\frac{24}{10-x} + \frac{28}{10+x} = 6\).
4. Testing \(x = 4\): \(\frac{24}{6} + \frac{28}{14} = 4 + 2 = 6\).
5. Since the equation holds, the stream speed is 4 km/h.
2. Upstream speed = \(10 - x\); Downstream speed = \(10 + x\).
3. Total time equation: \(\frac{24}{10-x} + \frac{28}{10+x} = 6\).
4. Testing \(x = 4\): \(\frac{24}{6} + \frac{28}{14} = 4 + 2 = 6\).
5. Since the equation holds, the stream speed is 4 km/h.
7.
A man can row 6 km/h in still water. If it takes him twice as long to row up as to row down the river, find the rate of the stream.
View Answer
Answer: Option A
Explanation:
Explanation:
1. Let the stream speed be \(s\). Then \(V_{up} = 6 - s\) and \(V_{down} = 6 + s\).
2. Time is inversely proportional to speed for the same distance. If Upstream time = \(2 \times\) Downstream time, then Downstream speed = \(2 \times\) Upstream speed.
3. Equation: \(6 + s = 2(6 - s)\).
4. \(6 + s = 12 - 2s \implies 3s = 6 \implies s = 2 \text{ km/h}\).
2. Time is inversely proportional to speed for the same distance. If Upstream time = \(2 \times\) Downstream time, then Downstream speed = \(2 \times\) Upstream speed.
3. Equation: \(6 + s = 2(6 - s)\).
4. \(6 + s = 12 - 2s \implies 3s = 6 \implies s = 2 \text{ km/h}\).
8.
A boat travels 12 km upstream in 4 hours and 12 km downstream in 3 hours. Find the speed of the stream.
View Answer
Answer: Option A
Explanation:
Explanation:
1. Upstream Speed (\(U\)) = \(12 / 4 = 3 \text{ km/h}\).
2. Downstream Speed (\(D\)) = \(12 / 3 = 4 \text{ km/h}\).
3. Speed of the stream = \(\frac{D - U}{2}\).
4. \(\text{Stream Speed} = \frac{4 - 3}{2} = 0.5 \text{ km/h}\).
2. Downstream Speed (\(D\)) = \(12 / 3 = 4 \text{ km/h}\).
3. Speed of the stream = \(\frac{D - U}{2}\).
4. \(\text{Stream Speed} = \frac{4 - 3}{2} = 0.5 \text{ km/h}\).
9.
A man can row 9 km/h in still water. It takes him 9 hours to row to a place 40 km distant and come back. Find the speed of the water.
View Answer
Answer: Option A
Explanation:
Explanation:
1. Let water speed be \(w\). \(V_{down} = 9 + w\), \(V_{up} = 9 - w\).
2. Total time = \(\frac{40}{9+w} + \frac{40}{9-w} = 9\).
3. \(40(9 - w + 9 + w) = 9(81 - w^2)\).
4. \(40(18) = 9(81 - w^2) \implies 720 = 729 - 9w^2\).
5. \(9w^2 = 9 \implies w^2 = 1 \implies w = 1 \text{ km/h}\).
2. Total time = \(\frac{40}{9+w} + \frac{40}{9-w} = 9\).
3. \(40(9 - w + 9 + w) = 9(81 - w^2)\).
4. \(40(18) = 9(81 - w^2) \implies 720 = 729 - 9w^2\).
5. \(9w^2 = 9 \implies w^2 = 1 \implies w = 1 \text{ km/h}\).
10.
A motorboat whose speed is 15 km/h in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. Find the speed of the stream.
View Answer
Answer: Option A
Explanation:
Explanation:
1. Total time = 4.5 hours. Let stream speed be \(x\).
2. Equation: \(\frac{30}{15+x} + \frac{30}{15-x} = 4.5\).
3. \(30(15 - x + 15 + x) = 4.5(225 - x^2)\).
4. \(900 = 1012.5 - 4.5x^2 \implies 4.5x^2 = 112.5\).
5. \(x^2 = 25 \implies x = 5 \text{ km/h}\).
2. Equation: \(\frac{30}{15+x} + \frac{30}{15-x} = 4.5\).
3. \(30(15 - x + 15 + x) = 4.5(225 - x^2)\).
4. \(900 = 1012.5 - 4.5x^2 \implies 4.5x^2 = 112.5\).
5. \(x^2 = 25 \implies x = 5 \text{ km/h}\).