Car cyclist pursuit

At 6.40, a cyclist started from the station at a speed of 12 km/h. At exactly 10:00, the car followed him at a speed of 84 km/h. What time does the car catch the cyclist?

Result

t = 10:33 hh:mm

Step-by-step explanation:

$$\begin{gathered} t_1=6\frac{40}{60}=6+\frac{40}{60}=\frac{6\cdot 60+40}{60}=\frac{360+40}{60}=\frac{400}{60}=\frac{20}{3}\doteq 6.6667\text{h} \\ {v}_1=12\text{km/h} \\ {t}_2=10.00\text{h} \\ {v}_2=84\text{km/h} \\ {s}_1=s_2 \\ {v}_1\cdot (t-t_1)=v_2\cdot (t-t_2) \\ 12\cdot (t-6.6666666666667)=84\cdot (t-10) \\ 72t=760 \\ t=\frac{760}{72}=10.55555556 \\ t=\frac{95}{9}\doteq 10.555556=10.55556=10:33\text{hh}:\text{mm} \end{gathered}$$

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