Tourist distance time

The tourist walked 1/4 of the way at a speed of 4.5 km/h, 2/5 at a speed of 4 km/h, and the remaining 7 km at a speed of 5 km/h. How many kilometers did he run, and how long did the journey take him? Calculate the time in a fraction.

Final Answer:

s =  20 km
t =  203/45 = 4 ²³⁄₄₅ h

Step-by-step explanation:

$$\begin{gathered} s_3=7\text{km} \\ \frac{s}{4}+\frac{2}{5}\cdot s+s_3=s \\ \frac{s}{4}+\frac{2}{5}\cdot s+7=s \\ s/4+2/5\cdot s+7=s \\ 7s=140 \\ s=\frac{140}{7}=20 \\ s=20=20\text{km} \end{gathered}$$

$$\begin{gathered} v_1=4.5\text{km/h} \\ {v}_2=4\text{km/h} \\ {v}_3=5\text{km/h} \\ {s}_1=s/4=20/4=5\text{km} \\ {s}_2=\frac{2}{5}\cdot s=\frac{2}{5}\cdot 20=\frac{2\cdot 20}{5}=\frac{40}{5}=8\text{km} \\ {t}_1=\frac{s_1}{v_1}=\frac{5}{4.5}=\frac{10}{9}\doteq 1.1111\text{h} \\ {t}_2=\frac{s_2}{v_2}=\frac{8}{4}=2\text{h} \\ {t}_3=\frac{s_3}{v_3}=\frac{7}{5}=1.4\text{h} \\ t=t_1+t_2+t_3=\frac{10}{9}+2+\frac{7}{5}=\frac{203}{45}\text{h}=4.5111\text{h} \end{gathered}$$

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