To solve the problem, you can use the Pythagorean theorem. Let's label the length of the ladder as "L", the height of the ladder on the wall as "x", and the distance between the bottom of the ladder and the wall as "y".

According to the Pythagorean theorem, we have:

x² + y² = L²

Differentiating both sides with respect to time, we get:

2x * dx/dt + 2y * dy/dt = 2L * dL/dt

Since we know the rate at which the length of the ladder is changing (dL/dt = -1 m/s), and we want to find the rate at which the bottom of the ladder is moving away from the wall (dy/dt when x = 6 m), we can rearrange the equation:

2x * dx/dt + 2y * dy/dt = 2L * dL/dt
2 * 6 * dx/dt + 2y * dy/dt = 2 * 10 * (-1)
12 * dx/dt + 2y * dy/dt = -20

Now, we need to find the value of y when x = 6 m. From the Pythagorean theorem, we know that when x = 6 m:

6² + y² = 10²
36 + y² = 100
y² = 100 - 36
y² = 64
y = 8

Using this value of y, we can substitute back into the equation and solve for dy/dt:

12 * dx/dt + 2y * dy/dt = -20
12 * dx/dt + 2 * 8 * dy/dt = -20
12 * dx/dt + 16 * dy/dt = -20
16 * dy/dt = -20 - 12 * dx/dt
dy/dt = (-20 - 12 * dx/dt) / 16

Plugging in the rate at which the length of the ladder is changing (dx/dt = -1 m/s), we get:

dy/dt = (-20 - 12 * (-1)) / 16
dy/dt = (-20 + 12) / 16
dy/dt = -8/16
dy/dt = -0.5 m/s

Therefore, the bottom of the ladder is moving away from the wall at a rate of 0.5 m/s when the top of the ladder is 6 meters above the ground.

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