Let the total distance be d km. Time = Distance ÷ Speed for each segment.<br><br>
&bull; First half (\frac{d}{2} km) at 50 km/h: time = \frac{d/2}{50} = \frac{d}{100} h<br>
&bull; Next quarter (\frac{d}{4} km) at 40 km/h: time = \frac{d/4}{40} = \frac{d}{160} h<br>
&bull; Final quarter (\frac{d}{4} km) at 80 km/h: time = \frac{d/4}{80} = \frac{d}{320} h<br>
&bull; Total time: \frac{d}{100} + \frac{d}{160} + \frac{d}{320} = 3<br>
&bull; LCD = 1600: \frac{16d}{1600} + \frac{10d}{1600} + \frac{5d}{1600} = 3<br>
&bull; \frac{31d}{1600} = 3<br>
&bull; d = 3 × \frac{1600}{31} = \frac{4800}{31}<br>
&bull; d &asymp; 154.84 km<br>
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Final Answer: 154.84 km