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A man can row at 8 km per hour in still water. If it takes him thrice as long to row upstream, as to row downstream, then find the stream velocity in km per hour.
(Important - Enter only the numerical value in the answer)
Correct answer is '4'. Can you explain this answer?
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A man can row at 8 km per hour in still water. If it takes him thrice ...
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A man can row at 8 km per hour in still water. If it takes him thrice ...
Solution:
Let's assume the speed of the stream is 'v' km/hr.
1. Speed of the man in still water:
The speed of the man in still water is given as 8 km/hr.
2. Speed of the man while rowing upstream:
When the man rows upstream, his effective speed reduces by the speed of the stream. So, the speed of the man while rowing upstream is (8 - v) km/hr.
3. Speed of the man while rowing downstream:
When the man rows downstream, his effective speed increases by the speed of the stream. So, the speed of the man while rowing downstream is (8 + v) km/hr.
4. Time taken to row upstream:
Let's assume the distance between the two points is 'd' km.
The time taken to row upstream can be calculated using the formula:
Time = Distance / Speed
So, the time taken to row upstream is d / (8 - v) hours.
5. Time taken to row downstream:
The time taken to row downstream can be calculated using the formula:
Time = Distance / Speed
So, the time taken to row downstream is d / (8 + v) hours.
6. Given condition:
According to the given condition, it takes the man thrice as long to row upstream as to row downstream. Mathematically, we can represent this as:
d / (8 - v) = 3 * (d / (8 + v))
7. Solving the equation:
Let's solve the above equation to find the value of 'v'.
Cross-multiplying the equation, we get:
3 * (8 - v) = 8 + v
Expanding the equation, we get:
24 - 3v = 8 + v
Bringing all the 'v' terms to one side and the constant terms to the other side, we get:
24 - 8 = v + 3v
16 = 4v
Dividing both sides by 4, we get:
v = 4
Therefore, the stream velocity is 4 km/hr.
Let's assume the speed of the stream is 'v' km/hr.
1. Speed of the man in still water:
The speed of the man in still water is given as 8 km/hr.
2. Speed of the man while rowing upstream:
When the man rows upstream, his effective speed reduces by the speed of the stream. So, the speed of the man while rowing upstream is (8 - v) km/hr.
3. Speed of the man while rowing downstream:
When the man rows downstream, his effective speed increases by the speed of the stream. So, the speed of the man while rowing downstream is (8 + v) km/hr.
4. Time taken to row upstream:
Let's assume the distance between the two points is 'd' km.
The time taken to row upstream can be calculated using the formula:
Time = Distance / Speed
So, the time taken to row upstream is d / (8 - v) hours.
5. Time taken to row downstream:
The time taken to row downstream can be calculated using the formula:
Time = Distance / Speed
So, the time taken to row downstream is d / (8 + v) hours.
6. Given condition:
According to the given condition, it takes the man thrice as long to row upstream as to row downstream. Mathematically, we can represent this as:
d / (8 - v) = 3 * (d / (8 + v))
7. Solving the equation:
Let's solve the above equation to find the value of 'v'.
Cross-multiplying the equation, we get:
3 * (8 - v) = 8 + v
Expanding the equation, we get:
24 - 3v = 8 + v
Bringing all the 'v' terms to one side and the constant terms to the other side, we get:
24 - 8 = v + 3v
16 = 4v
Dividing both sides by 4, we get:
v = 4
Therefore, the stream velocity is 4 km/hr.
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A man can row at 8 km per hour in still water. If it takes him thrice as long to row upstream,as to row downstream, then find the stream velocity in km per hour.(Important - Enter only the numerical value in the answer)Correct answer is '4'. Can you explain this answer?
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