Pedestrian up-down hill

The pedestrian goes for a walk first on the plane at 4 km/h, then uphill at 3 km/h. Then it is in the middle of the route, turns back, and goes downhill at 6 km/h. The total walk was 6 hours. How many kilometers went pedestrians?

Correct answer:

s =  24 km

Step-by-step explanation:

$$\begin{gathered} T=6\text{h} \\ c=1/2=\frac{1}{2}=0.5\text{h} \\ T=a+b+c+a \\ 4a+3b=6c+4a \\ 6=a+b+0.5+a \\ 4a+3b=6\cdot 0.5+4a \\ 6=a+b+0.5+a \\ 4\cdot a+3\cdot b=6\cdot 0.5+4\cdot a \\ 2a+b=5.5 \\ 3b=3 \\ b=\frac{3}{3}=1 \\ a=\frac{5.5-b}{2}=\frac{5.5-1}{2}=2.25 \\ a=\frac{9}{4}=2.25 \\ b=1 \\ s=4\cdot a+3\cdot b+6\cdot c+4\cdot a=4\cdot 2.25+3\cdot 1+6\cdot 0.5+4\cdot 2.25=24\text{km} \end{gathered}$$

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