Swimming pool

Thaddeus set off on foot to the swimming pool, which is 18 km from his residence. The trip took him two and a half hours. An hour later, his brother Viliam met him on his bicycle, whose journey took three-quarters of an hour.
a) Show the described situation graphically
b) Determine from the graph how many minutes Viliam will catch up with Thaddeus

Correct answer:

x =  25.7143 min

Step-by-step explanation:

$$\begin{gathered} s=18\text{km} \\ {t}_1=2.5\text{h} \\ {t}_2=\frac{3}{4}=0.75\text{h} \\ \Delta =1\text{h} \\ {s}_1=s_2 \\ {v}_1=s/t_1=18/2.5=\frac{36}{5}=7.2\text{km/h} \\ {v}_2=s/t_2=18/\frac{3}{4}=18:\frac{3}{4}=18\cdot \frac{4}{3}=\frac{18\cdot 4}{3}=\frac{72}{3}=24\text{km/h} \\ {v}_1\cdot (t+\Delta )=v_2\cdot t \\ 7.2\cdot (t+1)=24\cdot t \\ 16.8t=7.2 \\ t=\frac{7.2}{16.8}=0.42857143 \\ t=\frac{3}{7}\doteq 0.428571 \\ x=t\to \text{min}=t\cdot 60\text{min}=0.4286\cdot 60\text{min}=25.714\text{min}=\frac{180}{7}\text{min}=25.7143\text{min} \end{gathered}$$

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