Dirty road

Mr. Smith is on a road trip to a remote disc golf course 180km away. He travels part of the way at 100km/h along the highway and part of the way at 50km/h along dirt roads. If it took 2 hours to get there, how many hours did he spend on dirt roads?

Correct answer:

d =  20 km

Step-by-step explanation:

$$\begin{gathered} d+h=180 \\ d/50+h/100=2 \\ d+h=180 \\ 2d+h=200 \\ Pivot:Row1\leftrightarrow Row2 \\ 2d+h=200 \\ d+h=180 \\ Row2-\frac{1}{2}\cdot Row1\to Row2 \\ 2d+h=200 \\ 0.5h=80 \\ h=\frac{80}{0.5}=160 \\ d=\frac{200-h}{2}=\frac{200-160}{2}=20=20\text{km} \\ d=20 \\ h=160 \end{gathered}$$

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