1510.52 – Totem Pole

One-fifth of a totem pole is tapered at the top. One-sixth of the pole is buried in the ground. The remaining 3.8 meters are ornately carved. How high is the top of the totem pole above the ground?

Solution

Let $x$ represent the total length of the pole. Then $\dfrac{x}{5} + \dfrac{x}{6} + 3.8 = x$ .

So $\dfrac{11x}{30} + 3.8 = x$ . Multiplying through by 30, we get $11x + 114 = 30x$ , so $x = 6$ meters.

Since $\dfrac{1}{6}$ of the pole is buried underground, the top of the pole is 5 meters above the ground.