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Speed of a boat in still water is 9 km/hr. It goes 12 km downstream and comes back to the starting point in three hours. What is the speed of water in the stream?
- a)3 km/h
- b)4 km/h
- c)4.5 km/h
- d)5 km/h
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Speed of a boat in still water is 9 km/hr. It goes 12 km downstream an...
GIVEN:
Speed of boat in still water = 9km/h
Distance = 12km
Time to comes back to the starting Point = 3 hours
Speed of boat in still water = 9km/h
Distance = 12km
Time to comes back to the starting Point = 3 hours
FORMULA USED:
Upstream Speed = Speed of boat – Speed of Stream
Downstream Speed = Speed of boat + Speed of Stream
Time = Distance/speed
Upstream Speed = Speed of boat – Speed of Stream
Downstream Speed = Speed of boat + Speed of Stream
Time = Distance/speed
CALCULATION:
Let the speed of the boat = 9km/h
Speed of current = x km/h
Speed upstream = (9 – x) km/h
Speed downstream = (9 + x) km/h
Time upstream + Time downstream = 3 hours
12/(9 – x) + 12/(9 + x) = 3
x = 3 km/h
Let the speed of the boat = 9km/h
Speed of current = x km/h
Speed upstream = (9 – x) km/h
Speed downstream = (9 + x) km/h
Time upstream + Time downstream = 3 hours
12/(9 – x) + 12/(9 + x) = 3
x = 3 km/h
Most Upvoted Answer
Speed of a boat in still water is 9 km/hr. It goes 12 km downstream an...
Given:
Speed of boat in still water = 9 km/hr
To find:
Speed of water in the stream
Let's assume the speed of the stream is 'x' km/hr.
When the boat goes downstream, it gets a boost from the stream, so the effective speed becomes the sum of the speed of the boat in still water and the speed of the stream.
Effective speed downstream = Speed of boat in still water + Speed of stream = 9 + x km/hr
When the boat comes back upstream, it has to overcome the speed of the stream, so the effective speed becomes the difference between the speed of the boat in still water and the speed of the stream.
Effective speed upstream = Speed of boat in still water - Speed of stream = 9 - x km/hr
According to the given information, the boat travels 12 km downstream and comes back to the starting point in 3 hours. We can set up the following equation using the formula:
Time taken downstream + Time taken upstream = Total time
12/(9 + x) + 12/(9 - x) = 3
Simplifying the equation:
12(9 - x) + 12(9 + x) = 3(9 + x)(9 - x)
108 - 12x + 108 + 12x = 27 - x^2
216 = 27 - x^2
x^2 = 189
x = √189
x ≈ 13.75
Since the speed of the stream cannot be negative, we can discard the negative value. Therefore, the speed of the stream is approximately 13.75 km/hr.
But none of the given options match this value. Therefore, there might be an error in the question or options provided.
Speed of boat in still water = 9 km/hr
To find:
Speed of water in the stream
Let's assume the speed of the stream is 'x' km/hr.
When the boat goes downstream, it gets a boost from the stream, so the effective speed becomes the sum of the speed of the boat in still water and the speed of the stream.
Effective speed downstream = Speed of boat in still water + Speed of stream = 9 + x km/hr
When the boat comes back upstream, it has to overcome the speed of the stream, so the effective speed becomes the difference between the speed of the boat in still water and the speed of the stream.
Effective speed upstream = Speed of boat in still water - Speed of stream = 9 - x km/hr
According to the given information, the boat travels 12 km downstream and comes back to the starting point in 3 hours. We can set up the following equation using the formula:
Time taken downstream + Time taken upstream = Total time
12/(9 + x) + 12/(9 - x) = 3
Simplifying the equation:
12(9 - x) + 12(9 + x) = 3(9 + x)(9 - x)
108 - 12x + 108 + 12x = 27 - x^2
216 = 27 - x^2
x^2 = 189
x = √189
x ≈ 13.75
Since the speed of the stream cannot be negative, we can discard the negative value. Therefore, the speed of the stream is approximately 13.75 km/hr.
But none of the given options match this value. Therefore, there might be an error in the question or options provided.
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Speed of a boat in still water is 9 km/hr. It goes 12 km downstream and comes back to the starting point in three hours. What is the speed of water in the stream?a)3 km/hb)4 km/hc)4.5 km/hd)5 km/hCorrect answer is option 'A'. Can you explain this answer?
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