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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.
- a)2 km/hr
- b)4km/hr
- c)6km/hr
- d)8km/hr
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
A man can row at 8 km per hour in still water. If it takes him thrice ...
To solve this problem, let's first understand the concept of rowing upstream and downstream.
When a person rows in still water, the speed at which he rows is known as the speed in still water. Let's assume this speed is x km/h.
When the person rows downstream, the speed of the stream adds to his speed in still water, resulting in a faster speed. So, the speed downstream is (x + v) km/h, where v is the velocity of the stream.
On the other hand, when the person rows upstream, the speed of the stream subtracts from his speed in still water, resulting in a slower speed. So, the speed upstream is (x - v) km/h.
Now, let's solve the problem step by step.
Step 1: Given that the rowing speed in still water is 8 km/h.
Step 2: Let's assume the velocity of the stream is v km/h.
Step 3: To row downstream, the speed is (8 + v) km/h.
Step 4: To row upstream, the speed is (8 - v) km/h.
Step 5: According to the problem, it takes three times as long to row upstream as to row downstream.
Step 6: Let's assume the time taken to row downstream is t hours.
Step 7: The time taken to row upstream is 3t hours.
Step 8: Distance = Speed × Time.
Step 9: Distance downstream = (8 + v) × t.
Step 10: Distance upstream = (8 - v) × 3t.
Step 11: As per the problem, the distances downstream and upstream are the same.
Step 12: Therefore, (8 + v) × t = (8 - v) × 3t.
Step 13: Solving the above equation, we get v = 4 km/h.
Therefore, the stream velocity is 4 km/h, which is the correct answer (option B).
When a person rows in still water, the speed at which he rows is known as the speed in still water. Let's assume this speed is x km/h.
When the person rows downstream, the speed of the stream adds to his speed in still water, resulting in a faster speed. So, the speed downstream is (x + v) km/h, where v is the velocity of the stream.
On the other hand, when the person rows upstream, the speed of the stream subtracts from his speed in still water, resulting in a slower speed. So, the speed upstream is (x - v) km/h.
Now, let's solve the problem step by step.
Step 1: Given that the rowing speed in still water is 8 km/h.
Step 2: Let's assume the velocity of the stream is v km/h.
Step 3: To row downstream, the speed is (8 + v) km/h.
Step 4: To row upstream, the speed is (8 - v) km/h.
Step 5: According to the problem, it takes three times as long to row upstream as to row downstream.
Step 6: Let's assume the time taken to row downstream is t hours.
Step 7: The time taken to row upstream is 3t hours.
Step 8: Distance = Speed × Time.
Step 9: Distance downstream = (8 + v) × t.
Step 10: Distance upstream = (8 - v) × 3t.
Step 11: As per the problem, the distances downstream and upstream are the same.
Step 12: Therefore, (8 + v) × t = (8 - v) × 3t.
Step 13: Solving the above equation, we get v = 4 km/h.
Therefore, the stream velocity is 4 km/h, which is the correct answer (option B).
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Community Answer
A man can row at 8 km per hour in still water. If it takes him thrice ...
Speed of man (m) = 8km/h
Let the speed of stream be s
According to the question:
Speed of man upstream = S1= m − s
Speed of man downstream = S2 = m + s
Speed = Distance/Time
Here, since the distance D is same
D = S1 × T1
D = S2 × T2
S1 × T1 = S2 × T2
S1/S2 = T2/T1 = 3
m + s = 3(m − s)
or, 8 + s = 3(8 − s)
⇒ s = 4km/h
Let the speed of stream be s
According to the question:
Speed of man upstream = S1= m − s
Speed of man downstream = S2 = m + s
Speed = Distance/Time
Here, since the distance D is same
D = S1 × T1
D = S2 × T2
S1 × T1 = S2 × T2
S1/S2 = T2/T1 = 3
m + s = 3(m − s)
or, 8 + s = 3(8 − s)
⇒ s = 4km/h
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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.a)2 km/hrb)4km/hrc)6km/hrd)8km/hrCorrect answer is option 'B'. Can you explain this answer?
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