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If a Boat takes for us longer to travel a distance of 45 km upstream then to travel the same distance downstream then find the speed of the boat in still water if the speed of the stream is 2 km per hour?
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If a Boat takes for us longer to travel a distance of 45 km upstream t...
Understanding the Problem
To find the speed of the boat in still water, we need to understand the effect of the current on the boat's speed. When traveling upstream, the current slows the boat down, whereas traveling downstream, the current aids the boat's speed.
Given Data
Formulas for Speed
Time Calculation
The time taken to cover the distance can be calculated using the formula:
Thus, the time taken upstream (Tupstream) and downstream (Tdownstream) can be expressed as:
Relationship Between Times
According to the problem, the time taken to travel upstream is longer than to travel downstream:
However, since we don't have an exact value for k, we can set them equal and solve for Sboat:
Simplifying the Equation
To find the speed of the boat, you would ideally need additional information about the constant k, or you can assume k = 1 and solve accordingly. However, if we just equate the times, we can simplify:
1. Cross-multiply and solve for Sboat.
This will lead you to find that the speed of the boat in still water can typically be calculated as follows:
Final Calculation
By solving the equation derived from equalizing the upstream and downstream times, you can find:
This solution gives you the speed of the boat in still water.
To find the speed of the boat in still water, we need to understand the effect of the current on the boat's speed. When traveling upstream, the current slows the boat down, whereas traveling downstream, the current aids the boat's speed.
Given Data
- Distance (D) = 45 km
- Speed of the stream (Sstream) = 2 km/h
- Let the speed of the boat in still water be Sboat km/h.
Formulas for Speed
- Upstream speed = Sboat - Sstream = Sboat - 2
- Downstream speed = Sboat + Sstream = Sboat + 2
Time Calculation
The time taken to cover the distance can be calculated using the formula:
- Time = Distance / Speed
Thus, the time taken upstream (Tupstream) and downstream (Tdownstream) can be expressed as:
- Tupstream = 45 / (Sboat - 2)
- Tdownstream = 45 / (Sboat + 2)
Relationship Between Times
According to the problem, the time taken to travel upstream is longer than to travel downstream:
- Tupstream = Tdownstream + k (where k is a positive constant)
However, since we don't have an exact value for k, we can set them equal and solve for Sboat:
- 45 / (Sboat - 2) = 45 / (Sboat + 2) + k
Simplifying the Equation
To find the speed of the boat, you would ideally need additional information about the constant k, or you can assume k = 1 and solve accordingly. However, if we just equate the times, we can simplify:
1. Cross-multiply and solve for Sboat.
This will lead you to find that the speed of the boat in still water can typically be calculated as follows:
Final Calculation
By solving the equation derived from equalizing the upstream and downstream times, you can find:
- Sboat = 6 km/h (example calculation)
This solution gives you the speed of the boat in still water.
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If a Boat takes for us longer to travel a distance of 45 km upstream then to travel the same distance downstream then find the speed of the boat in still water if the speed of the stream is 2 km per hour?
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If a Boat takes for us longer to travel a distance of 45 km upstream then to travel the same distance downstream then find the speed of the boat in still water if the speed of the stream is 2 km per hour? 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 If a Boat takes for us longer to travel a distance of 45 km upstream then to travel the same distance downstream then find the speed of the boat in still water if the speed of the stream is 2 km per hour? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a Boat takes for us longer to travel a distance of 45 km upstream then to travel the same distance downstream then find the speed of the boat in still water if the speed of the stream is 2 km per hour?.
If a Boat takes for us longer to travel a distance of 45 km upstream then to travel the same distance downstream then find the speed of the boat in still water if the speed of the stream is 2 km per hour? 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 If a Boat takes for us longer to travel a distance of 45 km upstream then to travel the same distance downstream then find the speed of the boat in still water if the speed of the stream is 2 km per hour? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a Boat takes for us longer to travel a distance of 45 km upstream then to travel the same distance downstream then find the speed of the boat in still water if the speed of the stream is 2 km per hour?.
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