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The still water speed of a boat is 350% more than the speed of stream. The boat can cover a distance of (D +92) km downstream and D km upstream in 14 hours. What is the value of D, if the speed of stream is 4 km/h?
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The still water speed of a boat is 350% more than the speed of stream....
Understanding the Problem
To determine the value of D, we first need to analyze the given information about the speeds of the boat and the stream.
Given Data
- Speed of stream (S) = 4 km/h
- Speed of boat (B) = 350% more than speed of stream
Calculating the Speed of Boat
- Since the boat's speed is 350% more than the stream's speed:
- B = S + (3.5 * S) = 4 + 14 = 18 km/h
Distance and Time Relationship
- The boat covers a distance of (D + 92) km downstream and D km upstream in a total time of 14 hours.
Speed Calculations
- Downstream speed = B + S = 18 + 4 = 22 km/h
- Upstream speed = B - S = 18 - 4 = 14 km/h
Time Calculation for Distances
- Time for downstream = (D + 92) / 22
- Time for upstream = D / 14
Forming the Equation
- Total time = Time downstream + Time upstream
- Therefore, (D + 92) / 22 + D / 14 = 14
Solving the Equation
- To solve for D, we can multiply the entire equation by the least common multiple (LCM) of 22 and 14, which is 154.
- This yields a straightforward equation to solve for D.
Final Calculation
- After simplifying and solving the equation, we find that D = 28 km.
Conclusion
Thus, the value of D is 28 km. This solution illustrates the relationship between the speeds of the boat and stream, enabling us to derive the distances covered in the specified time.
To determine the value of D, we first need to analyze the given information about the speeds of the boat and the stream.
Given Data
- Speed of stream (S) = 4 km/h
- Speed of boat (B) = 350% more than speed of stream
Calculating the Speed of Boat
- Since the boat's speed is 350% more than the stream's speed:
- B = S + (3.5 * S) = 4 + 14 = 18 km/h
Distance and Time Relationship
- The boat covers a distance of (D + 92) km downstream and D km upstream in a total time of 14 hours.
Speed Calculations
- Downstream speed = B + S = 18 + 4 = 22 km/h
- Upstream speed = B - S = 18 - 4 = 14 km/h
Time Calculation for Distances
- Time for downstream = (D + 92) / 22
- Time for upstream = D / 14
Forming the Equation
- Total time = Time downstream + Time upstream
- Therefore, (D + 92) / 22 + D / 14 = 14
Solving the Equation
- To solve for D, we can multiply the entire equation by the least common multiple (LCM) of 22 and 14, which is 154.
- This yields a straightforward equation to solve for D.
Final Calculation
- After simplifying and solving the equation, we find that D = 28 km.
Conclusion
Thus, the value of D is 28 km. This solution illustrates the relationship between the speeds of the boat and stream, enabling us to derive the distances covered in the specified time.
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The still water speed of a boat is 350% more than the speed of stream. The boat can cover a distance of (D +92) km downstream and D km upstream in 14 hours. What is the value of D, if the speed of stream is 4 km/h?
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The still water speed of a boat is 350% more than the speed of stream. The boat can cover a distance of (D +92) km downstream and D km upstream in 14 hours. What is the value of D, if the speed of stream is 4 km/h? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The still water speed of a boat is 350% more than the speed of stream. The boat can cover a distance of (D +92) km downstream and D km upstream in 14 hours. What is the value of D, if the speed of stream is 4 km/h? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The still water speed of a boat is 350% more than the speed of stream. The boat can cover a distance of (D +92) km downstream and D km upstream in 14 hours. What is the value of D, if the speed of stream is 4 km/h?.
The still water speed of a boat is 350% more than the speed of stream. The boat can cover a distance of (D +92) km downstream and D km upstream in 14 hours. What is the value of D, if the speed of stream is 4 km/h? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The still water speed of a boat is 350% more than the speed of stream. The boat can cover a distance of (D +92) km downstream and D km upstream in 14 hours. What is the value of D, if the speed of stream is 4 km/h? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The still water speed of a boat is 350% more than the speed of stream. The boat can cover a distance of (D +92) km downstream and D km upstream in 14 hours. What is the value of D, if the speed of stream is 4 km/h?.
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