Cottage distance calculation

Karel left for the cottage at 7:00 and his parents 20 minutes later. Everyone came to the chat at the same time. Karel rode a motorcycle at a speed of 20 km/h, and his parents drove a car at 1 km per minute. How far is the cottage from where they live? When did they come to the cottage?

Result

s =  10 km
t₂ = 7:30 hh:mm

Step-by-step explanation:

$$\begin{gathered} v_1=20\text{km/h} \\ {v}_2=1\cdot 60=60\text{km/h} \\ {s}_1=s_2 \\ {v}_1\cdot t=v_2\cdot (t-20/60) \\ 20\cdot t=60\cdot (t-20/60) \\ 2400t=1200 \\ t=\frac{1200}{2400}=0.5 \\ t=\frac{1}{2}=0.5 \\ s=v_1\cdot t=20\cdot 0.5=10\text{km} \end{gathered}$$

$t_2=t+7.00=0.5+7.00=\frac{15}{2}=7.5=7:30\text{hh}:\text{mm}$

Try another example