Final answer:
The ratio of the speed of the boat in still water to the speed of the stream is 3:1, as the time taken to row upstream is twice the time taken downstream. This is calculated using the time-distance relationship and solving the equation derived from the given condition.
Step-by-step explanation:
The question at hand involves determining the ratio of the speed of the boat in still water to the speed of the stream, given that a man takes twice as long to row against the stream as with the stream. Let's use v to represent the speed of the boat in still water and u to represent the speed of the stream.
When rowing downstream, the boat's effective speed is v + u, and when rowing upstream, it is v - u. It is given that the time to row upstream is twice that of the time to row downstream. Using the formula time = distance/speed, we can write the following equation given that the distance is the same:
2 * (distance / (v + u)) = distance / (v - u)
On canceling the distances and rearranging the terms, we get:
2(v - u) = v + u
Further simplification leads to v = 3u, which gives us the ratio of the speed of the boat to the stream as 3:1.
The correct answer is (b) 3 : 1.