A six foot person is walking away from an 18 foot pole. Express the distance between the pole and the person in terms of the length of the persons shadow.
To express the distance between the pole and the person in terms of the length of the person's shadow, we can use similar triangles.
Let's denote the length of the person's shadow as "x". Since the person is six feet tall and the pole is 18 feet tall, we have the following proportion:
6 feet (height of the person) / x (length of the shadow) = 18 feet (height of the pole) / (x + 6 feet)
We can now solve this proportion to find the value of "x":
6 / x = 18 / (x + 6)
We can cross-multiply and solve for "x":
6 * (x + 6) = 18 * x
6x + 36 = 18x
36 = 18x - 6x
36 = 12x
x = 36 / 12
x = 3
Therefore, the length of the person's shadow is 3 feet. Since the person is walking away from the pole, the distance between the pole and the person would be the sum of the person's height (6 feet) and the length of their shadow (3 feet), which is 9 feet.