A man takes twice as long to row a distance against the stream as to r...
Given:
- A man takes twice as long to row a distance against the stream as to row the same distance in favor of the stream.
To find:
- The ratio of the speed of the boat (in still water) and the stream.
Explanation:
Let's assume the speed of the boat in still water is 'b' units and the speed of the stream is 's' units.
Speed in favor of the stream:
When rowing in the direction of the stream, the effective speed of the boat is increased by the speed of the stream. So, the speed of the boat in this case is (b + s) units.
Speed against the stream:
When rowing against the stream, the effective speed of the boat is decreased by the speed of the stream. So, the speed of the boat in this case is (b - s) units.
Time taken:
Let's assume that the distance is 'd' units.
- Time taken to row in favor of the stream = d / (b + s) units
- Time taken to row against the stream = d / (b - s) units
As per the given information, the man takes twice as long to row against the stream as to row in favor of the stream. Mathematically, this can be represented as:
d / (b - s) = 2 * (d / (b + s))
Simplifying the equation:
Multiplying both sides of the equation by (b + s) and (b - s) to eliminate the denominators:
d * (b + s) = 2 * d * (b - s)
Simplifying further:
b + s = 2b - 2s
Rearranging the terms:
3s = b
Conclusion:
The ratio of the speed of the boat (in still water) and the stream is 3:1. Therefore, option 'A' is the correct answer.