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Compound Curve 816748

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1. **State the problem:** We are given a compound curve with two elements: - First curve: $l_1 = 68^\circ$, $D_1 = 5^\circ$ - Second curve: $l_2 = 23^\circ$, $D_2 = 3^\circ$ The station of the Point of Intersection (PI) is 47+681, which is $47681$ in numeric form. We need to find the station of the Point of Curvature of the Compound curve (PCC). 2. **Formula and rules:** The length of a curve $L$ is related to its central angle $l$ and degree of curve $D$ by: $$L = \frac{l}{D} \times 100$$ where $l$ and $D$ are in degrees. 3. **Calculate lengths of each curve:** For the first curve: $$L_1 = \frac{68}{5} \times 100 = 13.6 \times 100 = 1360$$ For the second curve: $$L_2 = \frac{23}{3} \times 100 = \frac{23}{3} \times 100 = 7.6667 \times 100 = 766.667$$ 4. **Calculate total length of the compound curve:** $$L = L_1 + L_2 = 1360 + 766.667 = 2126.667$$ 5. **Determine station of PCC:** PCC is located before PI by the length of the compound curve, so: $$\text{Station of PCC} = \text{Station of PI} - L = 47681 - 2126.667 = 45554.333$$ 6. **Convert station back to standard format:** Station = 45554.333 means 455+54.333, or 45554.333 without the plus sign. **Final answer:** $$\boxed{45554.333}$$