Cyclist vs car

The cyclist rode out of the city at 18 km/h. One hour 30 minutes behind him started the car and caught up with the cyclist in 50 minutes.
How fast was driving the car? Where (what kilometer) from the city car overtook a cyclist?

Correct answer:

v₂ =  50.4 km/h
s =  42 km

Step-by-step explanation:

$$\begin{gathered} v_1=18\text{km/h} \\ {t}_1=1:30=1hr30min=1+\frac{30}{60}=1.5hr=1.5 \\ {t}_2=0:50=0hr50min=0+\frac{50}{60}=0.8333hr\doteq 0.8333 \\ s=v_1\cdot (t_1+t_2)=18\cdot (\frac{3}{2}+\frac{5}{6})=42\text{km} \\ s=v_2\cdot t_2 \\ {v}_2=\frac{s}{t_2}=\frac{42}{\frac{5}{6}}=\frac{252}{5}\text{km/h}=50.4\text{km/h} \end{gathered}$$

Try another example