Representation 80447

On the school ski trip, the team set off from hut A at 9:30 a.m. to hut B at a speed of 2 m/s. Fifteen minutes later, the instructor followed them at a speed of 3 m/s. At what time and distance from cabin A will the instructor catch up with the team?
Please use graphical representation and calculation according to the formula.

Result

t = 10:15 hh:mm

Step-by-step explanation:

$$\begin{gathered} t_1=9:30=9hr30min=9+\frac{30}{60}=9.5hr=9.5 \\ {v}_1=2\text{m/s}\to \text{km/h}=2\cdot 3.6\text{km/h}=7.2\text{km/h} \\ {t}_2=t_1+15/60=9.5+15/60=\frac{39}{4}=9.75\text{h} \\ {v}_2=3\text{m/s}\to \text{km/h}=3\cdot 3.6\text{km/h}=10.8\text{km/h} \\ {s}_1=s_2 \\ {v}_1\cdot (t-t_1)=v_2\cdot (t-t_2) \\ 7.2\cdot (t-9.5)=10.8\cdot (t-9.75) \\ 3.6t=36.9 \\ t=\frac{36.9}{3.6}=10.25 \\ t=\frac{41}{4}=10.25=10:15\text{hh}:\text{mm} \end{gathered}$$

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