Final answer:
The speed of the stream cannot be determined based on the given information.
Step-by-step explanation:
To find the speed of the stream, we can set up two equations using the given information.
Let's assume the speed of the stream is 's' km/h.
When traveling upstream (against the current), the effective speed of the boat is reduced by the speed of the stream. So the boat speed is (5 - s) km/h.
When traveling downstream (with the current), the effective speed of the boat is increased by the speed of the stream. So the boat speed is (5 + s) km/h.
Using the formula: Time = Distance / Speed, we can set up the following equations:
15 / (5 - s) + 28 / (5 + s) = 5
Simplifying the equation:Expanding and simplifying:(75 + 15s + 140 - 28s) / (25 - s^2) = 5Combine like terms:(215 - 13s) / (25 - s^2) = 5Cross multiply:215 - 13s = 5(25 - s^2)Expand and simplify:215 - 13s = 125 - 5s^2Rearrange the equation:5s^2 - 13s + 90 = 0Use the quadratic formula to solve for s:s = (-(-13) ± sqrt((-13)^2 - 4(5)(90))) / 2(5)s = (13 ± sqrt(169 - 180)) / 10s = (13 ± sqrt(-11)) / 10The square root of a negative number is not real, so there is no solution. This means that there is no speed of the stream that satisfies the given conditions.