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A boat takes 26 hours for travelling downstream from point A to point B and coming back to point C midway between A and B. If the velocity of the stream is 4 km/hr and the speed of the boat in still water is 10 km/hr, what is the distance between A and B?
- a)210km
- b)185km
- c)140 km
- d)168km
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
A boat takes 26 hours for travelling downstream from point A to point ...
Let's break down the problem and solve it step by step.
Given information:
- Velocity of the stream = 4 km/hr
- Speed of the boat in still water = 10 km/hr
- Time taken for downstream journey (A to B and back to C) = 26 hours
To find:
- Distance between points A and B
Understanding the problem:
The boat is traveling downstream from point A to point B. Downstream refers to the direction of the stream's flow. When the boat travels downstream, the speed of the stream is added to the speed of the boat in still water, resulting in a faster speed. On the return journey from B to C, the boat is traveling upstream, against the stream's flow. When the boat travels upstream, the speed of the stream is subtracted from the speed of the boat in still water, resulting in a slower speed.
Let's calculate the speed of the boat relative to the stream in both cases:
- Downstream speed = Speed of the boat in still water + Velocity of the stream = 10 km/hr + 4 km/hr = 14 km/hr
- Upstream speed = Speed of the boat in still water - Velocity of the stream = 10 km/hr - 4 km/hr = 6 km/hr
Calculating the distance:
We know that time taken for the downstream journey + time taken for the upstream journey = 26 hours.
Let the distance between A and B be x km.
- Time taken for the downstream journey: Distance/Speed = x/14 hours
- Time taken for the upstream journey: Distance/Speed = x/6 hours
According to the given information, the downstream journey and the upstream journey together take 26 hours:
x/14 + x/6 = 26
To solve this equation, we can find a common denominator:
(6x + 14x)/84 = 26
20x = 26 * 84
20x = 2184
x = 2184/20
x = 109.2 km
Therefore, the distance between A and B is approximately 109.2 km. However, since the options provided are in whole numbers, we can round this value to the nearest whole number, which is 109 km.
As none of the given options match the calculated distance, it seems there might be a mistake in the options provided.
Given information:
- Velocity of the stream = 4 km/hr
- Speed of the boat in still water = 10 km/hr
- Time taken for downstream journey (A to B and back to C) = 26 hours
To find:
- Distance between points A and B
Understanding the problem:
The boat is traveling downstream from point A to point B. Downstream refers to the direction of the stream's flow. When the boat travels downstream, the speed of the stream is added to the speed of the boat in still water, resulting in a faster speed. On the return journey from B to C, the boat is traveling upstream, against the stream's flow. When the boat travels upstream, the speed of the stream is subtracted from the speed of the boat in still water, resulting in a slower speed.
Let's calculate the speed of the boat relative to the stream in both cases:
- Downstream speed = Speed of the boat in still water + Velocity of the stream = 10 km/hr + 4 km/hr = 14 km/hr
- Upstream speed = Speed of the boat in still water - Velocity of the stream = 10 km/hr - 4 km/hr = 6 km/hr
Calculating the distance:
We know that time taken for the downstream journey + time taken for the upstream journey = 26 hours.
Let the distance between A and B be x km.
- Time taken for the downstream journey: Distance/Speed = x/14 hours
- Time taken for the upstream journey: Distance/Speed = x/6 hours
According to the given information, the downstream journey and the upstream journey together take 26 hours:
x/14 + x/6 = 26
To solve this equation, we can find a common denominator:
(6x + 14x)/84 = 26
20x = 26 * 84
20x = 2184
x = 2184/20
x = 109.2 km
Therefore, the distance between A and B is approximately 109.2 km. However, since the options provided are in whole numbers, we can round this value to the nearest whole number, which is 109 km.
As none of the given options match the calculated distance, it seems there might be a mistake in the options provided.
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Community Answer
A boat takes 26 hours for travelling downstream from point A to point ...
- As per the given information, the velocity of the stream is 4 km/hr.
- The speed of the boat in still water is 10 km/hr.
- Therefore, speed of boat in downstream = (10+4)= 14km/hr
- The speed of boat in upstream = (10-4) = 6 km/hr.
- Let the distance between A and B be 'x'. As C is the distance between B and C is x/2.
- Total time taken to reach is 26 hours.
Therefore,
x/14 + (x/2)/6 = 26
⇒ x/14 + x/12 = 26
⇒ (7x+6x)/84 = 26
⇒ 13 x /84 = 26
⇒ x/84 = 2
⇒ x = 168.
The distance between A and B is 168 km.
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A boat takes 26 hours for travelling downstream from point A to point B and coming back to point C midway between A and B. If the velocity of the stream is 4 km/hr and the speed of the boat in still water is 10 km/hr, what is the distance between A and B?a)210kmb)185kmc)140 kmd)168kmCorrect answer is option 'D'. Can you explain this answer?
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A boat takes 26 hours for travelling downstream from point A to point B and coming back to point C midway between A and B. If the velocity of the stream is 4 km/hr and the speed of the boat in still water is 10 km/hr, what is the distance between A and B?a)210kmb)185kmc)140 kmd)168kmCorrect answer is option 'D'. Can you explain this answer? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about A boat takes 26 hours for travelling downstream from point A to point B and coming back to point C midway between A and B. If the velocity of the stream is 4 km/hr and the speed of the boat in still water is 10 km/hr, what is the distance between A and B?a)210kmb)185kmc)140 kmd)168kmCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A boat takes 26 hours for travelling downstream from point A to point B and coming back to point C midway between A and B. If the velocity of the stream is 4 km/hr and the speed of the boat in still water is 10 km/hr, what is the distance between A and B?a)210kmb)185kmc)140 kmd)168kmCorrect answer is option 'D'. Can you explain this answer?.
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A boat takes 26 hours for travelling downstream from point A to point B and coming back to point C midway between A and B. If the velocity of the stream is 4 km/hr and the speed of the boat in still water is 10 km/hr, what is the distance between A and B?a)210kmb)185kmc)140 kmd)168kmCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for A boat takes 26 hours for travelling downstream from point A to point B and coming back to point C midway between A and B. If the velocity of the stream is 4 km/hr and the speed of the boat in still water is 10 km/hr, what is the distance between A and B?a)210kmb)185kmc)140 kmd)168kmCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of A boat takes 26 hours for travelling downstream from point A to point B and coming back to point C midway between A and B. If the velocity of the stream is 4 km/hr and the speed of the boat in still water is 10 km/hr, what is the distance between A and B?a)210kmb)185kmc)140 kmd)168kmCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
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