Kilometers 4604

The tourist traveled 78 km in three hours. For part of the journey, he traveled by bus at an average speed of 30 km/h, and for the rest, he walked at an average speed of 6 km/h. How long did he walk, and how many kilometers did he walk?

Correct answer:

t₂ =  0.5 h
s₂ =  3 km

Step-by-step explanation:

$$\begin{gathered} s=78 \\ t=3 \\ {v}_1=30 \\ {v}_2=6 \\ {s}_1+s_2=s \\ {v}_1{t}_1+v_2{t}_2=s \\ {v}_1(t-t_2)+v_2{t}_2=s \\ {t}_2=(s-v_1\cdot t)/(v_2-v_1)=(78-30\cdot 3)/(6-30)=0.5\text{h} \end{gathered}$$

$$\begin{gathered} t_1=t-t_2=3-0.5=\frac{5}{2}=2.5 \\ {s}_1=v_1\cdot t_1=30\cdot 2.5=75 \\ {s}_2=t_2\cdot v_2=0.5\cdot 6=3\text{km} \end{gathered}$$

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