The tourist

The tourist will cross a 5 km long section in 3 hours. Part of the journey goes at a speed of 0.8 m/s and the other part at a speed of 0.4 m/s. Find the length of the first and second parts of the journey.

Final Answer:

a =  1.36 km
b =  3.64 km

Step-by-step explanation:

$$\begin{gathered} s=5\text{km} \\ t=3\text{h} \\ {v}_1=0.8\text{m/s}\to \text{km/h}=0.8\cdot 3.6\text{km/h}=2.88\text{km/h} \\ {v}_2=0.4\text{m/s}\to \text{km/h}=0.4\cdot 3.6\text{km/h}=1.44\text{km/h} \\ s=a+b \\ a=v_1\cdot t_1 \\ b=v_2\cdot t_2 \\ t=t_1+t_2 \\ s=v_1\cdot t_1+v_2\cdot (t-t_1) \\ 5=2.88\cdot t_1+1.44\cdot (3-t_1) \\ 1.44t_1=0.68 \\ {t}_1=\frac{0.68}{1.44}=0.47222222 \\ {t}_1=\frac{17}{36}\doteq 0.472222 \\ a=v_1\cdot t_1=2.88\cdot 0.4722=1.36\text{km} \end{gathered}$$

$b=s-a=5-1.36=3.64\text{km}$

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