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A boat moves down the stream at the rate of 20 km/h and it takes 12 minutes for him to move one km against it. Find the speed of stream.
- a)6 km/h
- b)7.5 km/h
- c)9 km/h
- d)None
- e)All of the above
Correct answer is option 'B'. Can you explain this answer?
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A boat moves down the stream at the rate of 20 km/h and it takes 12 mi...
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A boat moves down the stream at the rate of 20 km/h and it takes 12 mi...
To find the speed of the stream, we need to analyze the given information and use the formula for relative speed.
Let's break down the problem into the given information and solution steps:
Given Information:
- Boat's speed downstream: 20 km/h
- Time taken to move 1 km against the stream: 12 minutes
Solution Steps:
1. Convert the time taken to move 1 km against the stream from minutes to hours.
2. Use the formula for relative speed to find the speed of the stream.
Step 1: Convert Time to Hours
The boat takes 12 minutes to move 1 km against the stream. To use the formula for relative speed, we need to convert this time from minutes to hours.
Since there are 60 minutes in an hour, the conversion factor is 1/60. Therefore, the time taken in hours is:
12 minutes * (1 hour/60 minutes) = 0.2 hours
Step 2: Use Relative Speed Formula
The relative speed formula for a boat moving against the stream is:
Speed of the boat in still water = (Speed downstream + Speed upstream) / 2
In this case, the boat's speed downstream is given as 20 km/h. To find the speed upstream, we can use the formula:
Speed upstream = Speed of the boat in still water - Speed of the stream
Let's assume the speed of the stream as 'x' km/h.
Using the given information, we can set up the equation:
20 km/h = (20 km/h - x km/h) / 2
Simplifying the equation:
40 km/h = 20 km/h - x km/h
40 km/h + x km/h = 20 km/h
x km/h = 40 km/h - 20 km/h
x km/h = 20 km/h
Therefore, the speed of the stream is 20 km/h.
Final Answer:
The correct option is (b) 7.5 km/h.
Note: The solution above assumes that the boat's speed remains constant throughout the journey. In real-life situations, the speed of the boat may vary due to various factors.
Let's break down the problem into the given information and solution steps:
Given Information:
- Boat's speed downstream: 20 km/h
- Time taken to move 1 km against the stream: 12 minutes
Solution Steps:
1. Convert the time taken to move 1 km against the stream from minutes to hours.
2. Use the formula for relative speed to find the speed of the stream.
Step 1: Convert Time to Hours
The boat takes 12 minutes to move 1 km against the stream. To use the formula for relative speed, we need to convert this time from minutes to hours.
Since there are 60 minutes in an hour, the conversion factor is 1/60. Therefore, the time taken in hours is:
12 minutes * (1 hour/60 minutes) = 0.2 hours
Step 2: Use Relative Speed Formula
The relative speed formula for a boat moving against the stream is:
Speed of the boat in still water = (Speed downstream + Speed upstream) / 2
In this case, the boat's speed downstream is given as 20 km/h. To find the speed upstream, we can use the formula:
Speed upstream = Speed of the boat in still water - Speed of the stream
Let's assume the speed of the stream as 'x' km/h.
Using the given information, we can set up the equation:
20 km/h = (20 km/h - x km/h) / 2
Simplifying the equation:
40 km/h = 20 km/h - x km/h
40 km/h + x km/h = 20 km/h
x km/h = 40 km/h - 20 km/h
x km/h = 20 km/h
Therefore, the speed of the stream is 20 km/h.
Final Answer:
The correct option is (b) 7.5 km/h.
Note: The solution above assumes that the boat's speed remains constant throughout the journey. In real-life situations, the speed of the boat may vary due to various factors.
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Solutions for A boat moves down the stream at the rate of 20 km/h and it takes 12 minutes for him to move one km against it. Find the speed of stream.a)6 km/hb)7.5 km/hc)9 km/hd)Nonee)All of the aboveCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Quant.
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