Hiker average speed

The hiker walked for 3 hours at a 4 km/h speed. Due to the deteriorating weather, he increased his pace and walked at 7 km/h for the next hour and a half. At the end of his trip, it started to rain, so he started running at a speed of 20 km/h for 30 minutes. What was his average speed for the entire trip?

Final Answer:

v =  6.5 km/h

Step-by-step explanation:

$$\begin{gathered} t_1=3\text{h} \\ {v}_1=4\text{km/h} \\ {s}_1=v_1\cdot t_1=4\cdot 3=12\text{km} \\ {t}_2=1.5\text{h} \\ {v}_2=7\text{km/h} \\ {s}_2=v_2\cdot t_2=7\cdot 1.5=\frac{21}{2}=10.5\text{km} \\ {t}_3=30\text{min}\to \text{h}=30:60\text{h}=0.5\text{h} \\ {v}_3=20\text{km/h} \\ {s}_3=v_3\cdot t_3=20\cdot 0.5=10\text{km} \\ s=s_1+s_2+s_3=12+10.5+10=\frac{65}{2}=32.5\text{km} \\ t=t_1+t_2+t_3=3+1.5+0.5=5\text{h} \\ v=s/t=32.5/5=6.5\text{km/h} \end{gathered}$$

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