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The time taken by a swimmer to row upstream in a river is 5 times the time taken by him to row downstream. If the speed of boat in still water is 18 km/hr., then calculate the speed of the stream.
- a)12 km/hr.
- b)10 km/hr.
- c)8 km/hr.
- d)6 km/hr.
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The time taken by a swimmer to row upstream in a river is 5 times the ...
Let the speed of the boat in still water be B=18 km/hr, and let the speed of the stream be S km/hr.
Step 1: Define the upstream and downstream speeds
Downstream speed: When rowing downstream, the effective speed is the speed of the boat plus the speed of the stream. So, the downstream speed is:
Downstream speed=B+S=18+S km/hr
Upstream speed: When rowing upstream, the effective speed is the speed of the boat minus the speed of the stream. So, the upstream speed is:
Upstream speed=B−S=18−S km/hr
Step 2: Use the given condition
It is given that the time taken to row upstream is 5 times the time taken to row downstream. Since time = distance/speed, the ratio of times can be written as:
S+5S=90−18
6S=72
S=72/6=12 km/hr
Final Answer:
The speed of the stream is 12 km/hr.
So, the correct answer is: 1. 12 km/hr.
Most Upvoted Answer
The time taken by a swimmer to row upstream in a river is 5 times the ...
The question belongs to the "Time, Speed, and Distance" category in mathematics. We need to find the speed of the stream.
Let's assume the speed of the stream is 'x' km/hr.
Given:
Speed of boat in still water = 18 km/hr
Time taken to row upstream = 5 times the time taken to row downstream
To solve this problem, we can use the concept of relative speed. The relative speed of the boat with respect to the stream is the difference between the speed of the boat in still water and the speed of the stream.
1. Speed of the boat while rowing upstream:
The speed of the boat while rowing upstream is the speed of the boat in still water minus the speed of the stream. So, the speed of the boat while rowing upstream is (18 - x) km/hr.
2. Speed of the boat while rowing downstream:
The speed of the boat while rowing downstream is the speed of the boat in still water plus the speed of the stream. So, the speed of the boat while rowing downstream is (18 + x) km/hr.
3. Time taken to row upstream:
Let's assume the distance between the two points is 'd' km.
Time = Distance / Speed
Time taken to row upstream = d / (18 - x)
4. Time taken to row downstream:
Time taken to row downstream = d / (18 + x)
According to the given condition, the time taken to row upstream is 5 times the time taken to row downstream. So, we can write the equation:
d / (18 - x) = 5 * (d / (18 + x))
Simplifying the equation:
(18 + x) / (18 - x) = 5
Cross-multiplying:
18 + x = 5(18 - x)
18 + x = 90 - 5x
6x = 72
x = 12
Therefore, the speed of the stream is 12 km/hr.
Hence, the correct answer is option 'A' - 12 km/hr.
Let's assume the speed of the stream is 'x' km/hr.
Given:
Speed of boat in still water = 18 km/hr
Time taken to row upstream = 5 times the time taken to row downstream
To solve this problem, we can use the concept of relative speed. The relative speed of the boat with respect to the stream is the difference between the speed of the boat in still water and the speed of the stream.
1. Speed of the boat while rowing upstream:
The speed of the boat while rowing upstream is the speed of the boat in still water minus the speed of the stream. So, the speed of the boat while rowing upstream is (18 - x) km/hr.
2. Speed of the boat while rowing downstream:
The speed of the boat while rowing downstream is the speed of the boat in still water plus the speed of the stream. So, the speed of the boat while rowing downstream is (18 + x) km/hr.
3. Time taken to row upstream:
Let's assume the distance between the two points is 'd' km.
Time = Distance / Speed
Time taken to row upstream = d / (18 - x)
4. Time taken to row downstream:
Time taken to row downstream = d / (18 + x)
According to the given condition, the time taken to row upstream is 5 times the time taken to row downstream. So, we can write the equation:
d / (18 - x) = 5 * (d / (18 + x))
Simplifying the equation:
(18 + x) / (18 - x) = 5
Cross-multiplying:
18 + x = 5(18 - x)
18 + x = 90 - 5x
6x = 72
x = 12
Therefore, the speed of the stream is 12 km/hr.
Hence, the correct answer is option 'A' - 12 km/hr.
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The time taken by a swimmer to row upstream in a river is 5 times the time taken by him to row downstream. If the speed of boat in still water is 18 km/hr., then calculate the speed of the stream.a)12 km/hr.b)10 km/hr.c)8 km/hr.d)6 km/hr.Correct answer is option 'A'. Can you explain this answer?
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