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The speed of a boat in still water is 5 kilometers per hour. It can go 15 km upstream and 28 km downstream in 5 hours. Find the speed of the stream.

a) 2 km/h
b) 3 km/h
c) 4 km/h
d) 5 km/h

User Thameera
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1 Answer

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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.
User Tessaract
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