To solve this problem, we need to determine the speed of the stream based on the given information about the boat’s speed and its journey upstream and downstream.
Let the speed of the stream be x km/h. The speed of the boat going upstream will then be (11 – x) km/h, and the speed downstream will be (11 + x) km/h.
The distance covered in each direction is 12 km. The total time taken for the round trip is 2 hours and 45 minutes, which we can convert into hours: 2 hours and 45 minutes is equal to (2 + 45/60) = 2.75 hours.
We can use the formula for time, which is Time = Distance / Speed. The time taken to go upstream is:
Time upstream = Distance / Speed = 12 / (11 – x)
And the time taken to go downstream is:
Time downstream = Distance / Speed = 12 / (11 + x)
Adding these two times together gives us:
12 / (11 – x) + 12 / (11 + x) = 2.75
Now, we can solve this equation. First, let’s find a common denominator, which is (11 – x)(11 + x). So, we rewrite the equation as:
12(11 + x) + 12(11 – x) = 2.75(11 – x)(11 + x)
Expanding both sides results in:
12(11 + x) + 12(11 – x) = 12 * 11 + 12 * 11 = 264 (since the terms with x cancel out)
On the right side, simplifying yields:
2.75(121 – x^2) = 264
Now we can solve for x:
121 – x^2 = 264 / 2.75
Calculating gives us:
121 – x^2 ≈ 96
This leads to:
x^2 = 121 – 96 ≈ 25
Thus, we find:
x = 5
Therefore, the speed of the stream is 5 km/h.