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A motorboat covers the distance between two spots on the river in 8h and 12h downstream and upstream respectively .the time required by the boat to cover this distance in still water is?
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A motorboat covers the distance between two spots on the river in 8h a...
**Explanation:**
To find the time required by the boat to cover the distance in still water, we need to understand the concept of relative velocity.
**Relative Velocity:**
Relative velocity is the velocity of an object with respect to another object. It is the difference between the velocities of the two objects.
**Downstream and Upstream:**
When a boat is moving downstream, it is moving in the same direction as the current of the river. In this case, the boat's speed is increased by the speed of the current.
When a boat is moving upstream, it is moving against the current of the river. In this case, the boat's speed is decreased by the speed of the current.
**Let's solve the problem:**
Let's assume the speed of the boat in still water is 'b' and the speed of the current is 'c'.
1. **Downstream:**
- Time taken to cover the distance downstream = 8 hours
- Speed of the boat downstream = b + c (as the boat's speed is increased by the speed of the current)
- Distance = Speed × Time
- Distance = (b + c) × 8
2. **Upstream:**
- Time taken to cover the distance upstream = 12 hours
- Speed of the boat upstream = b - c (as the boat's speed is decreased by the speed of the current)
- Distance = Speed × Time
- Distance = (b - c) × 12
3. **Distance Covered:**
- The distance covered downstream is the same as the distance covered upstream.
- (b + c) × 8 = (b - c) × 12
4. **Solving the equation:**
- Expand the equation: 8b + 8c = 12b - 12c
- Simplify: 20c = 4b
- Divide both sides by 4: 5c = b
Therefore, the speed of the boat in still water is 5 times the speed of the current.
5. **Time in Still Water:**
- To find the time required by the boat to cover the distance in still water, we need to consider the distance covered and the speed in still water.
- Distance = Speed × Time
- Distance = b × t (where t is the time required in still water)
- Distance = (5c) × t (substituting b = 5c)
- Distance covered downstream = Distance covered upstream
- (b + c) × 8 = (b - c) × 12
- (5c + c) × 8 = (5c - c) × 12
- 6c × 8 = 4c × 12
- 48c = 48c
- The time required in still water is 8 hours.
Therefore, the time required by the boat to cover the distance in still water is 8 hours.
To find the time required by the boat to cover the distance in still water, we need to understand the concept of relative velocity.
**Relative Velocity:**
Relative velocity is the velocity of an object with respect to another object. It is the difference between the velocities of the two objects.
**Downstream and Upstream:**
When a boat is moving downstream, it is moving in the same direction as the current of the river. In this case, the boat's speed is increased by the speed of the current.
When a boat is moving upstream, it is moving against the current of the river. In this case, the boat's speed is decreased by the speed of the current.
**Let's solve the problem:**
Let's assume the speed of the boat in still water is 'b' and the speed of the current is 'c'.
1. **Downstream:**
- Time taken to cover the distance downstream = 8 hours
- Speed of the boat downstream = b + c (as the boat's speed is increased by the speed of the current)
- Distance = Speed × Time
- Distance = (b + c) × 8
2. **Upstream:**
- Time taken to cover the distance upstream = 12 hours
- Speed of the boat upstream = b - c (as the boat's speed is decreased by the speed of the current)
- Distance = Speed × Time
- Distance = (b - c) × 12
3. **Distance Covered:**
- The distance covered downstream is the same as the distance covered upstream.
- (b + c) × 8 = (b - c) × 12
4. **Solving the equation:**
- Expand the equation: 8b + 8c = 12b - 12c
- Simplify: 20c = 4b
- Divide both sides by 4: 5c = b
Therefore, the speed of the boat in still water is 5 times the speed of the current.
5. **Time in Still Water:**
- To find the time required by the boat to cover the distance in still water, we need to consider the distance covered and the speed in still water.
- Distance = Speed × Time
- Distance = b × t (where t is the time required in still water)
- Distance = (5c) × t (substituting b = 5c)
- Distance covered downstream = Distance covered upstream
- (b + c) × 8 = (b - c) × 12
- (5c + c) × 8 = (5c - c) × 12
- 6c × 8 = 4c × 12
- 48c = 48c
- The time required in still water is 8 hours.
Therefore, the time required by the boat to cover the distance in still water is 8 hours.
Community Answer
A motorboat covers the distance between two spots on the river in 8h a...
9.6 h
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A motorboat covers the distance between two spots on the river in 8h and 12h downstream and upstream respectively .the time required by the boat to cover this distance in still water is?
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A motorboat covers the distance between two spots on the river in 8h and 12h downstream and upstream respectively .the time required by the boat to cover this distance in still water is? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A motorboat covers the distance between two spots on the river in 8h and 12h downstream and upstream respectively .the time required by the boat to cover this distance in still water is? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A motorboat covers the distance between two spots on the river in 8h and 12h downstream and upstream respectively .the time required by the boat to cover this distance in still water is?.
A motorboat covers the distance between two spots on the river in 8h and 12h downstream and upstream respectively .the time required by the boat to cover this distance in still water is? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A motorboat covers the distance between two spots on the river in 8h and 12h downstream and upstream respectively .the time required by the boat to cover this distance in still water is? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A motorboat covers the distance between two spots on the river in 8h and 12h downstream and upstream respectively .the time required by the boat to cover this distance in still water is?.
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