Let's call the speed of the river flow as r km/h.
Since the boat is rowing directly across the river, its speed relative to the river flow is 5 km/h. So, we can say:
Speed of the boat in still water + Speed of the river flow = Speed of the boat relative to the river flow
Let's represent the speed of the boat in still water as b km/h.
Using the equation mentioned above, we can rewrite it as:
b + r = 5
Now, we know that the boat is rowing at an angle across the river. This means that its speed relative to the ground will be different.
To find the speed of the boat relative to the ground, we can use the Pythagorean theorem. The Pythagorean theorem states that the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). In this case, the speed of the boat relative to the ground (c) is the hypotenuse, while the speed of the boat relative to the river flow (b) is one side, and the speed of the river flow (r) is the other side.
c^2 = b^2 + r^2
Substituting the value of b from the first equation, we get:
(5 - r)^2 = b^2 + r^2
Expanding the equation, we get:
25 - 10r + r^2 = b^2 + r^2
Simplifying the equation, we get:
25 - 10r = b^2
From the equation b + r = 5, we can rearrange it to solve for b:
b = 5 - r
Substituting this value of b in the equation 25 - 10r = b^2, we get:
25 - 10r = (5 - r)^2
Expanding the equation, we get:
25 - 10r = 25 - 10r + r^2
Canceling out common terms, we get:
0 = r^2
This equation implies that r = 0, which means there is no river flow.
Therefore, the speed of the river flow is 0 km/h.
A boat rowed with a speed of 5kmph directly across a river flowing
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