Motorcyclist and cyclist

At noon, a cyclist left Šumperk for Olomouc at a 20 km/h speed. Thirty minutes later, a motorcyclist drove up behind him at 60 km/h. At what distance and at what time did the motorcyclist overtake the cyclist?

Result

s =  15 km
t = 12:45 hh:mm

Step-by-step explanation:

$$\begin{gathered} v_1=20\text{km/h} \\ {v}_2=60\text{km/h} \\ s=v_1\cdot (t-12) \\ s=v_2\cdot (t-12.50) \\ {v}_1\cdot (t-12)=v_2\cdot (t-12.50) \\ 20\cdot (t-12)=60\cdot (t-12.50) \\ 40t=510 \\ t=\frac{510}{40}=12.75 \\ t=\frac{51}{4}=12.75 \\ s=v_1\cdot (t-12)=20\cdot (12.75-12)=15\text{km} \end{gathered}$$

$t=12.75=\frac{51}{4}=12:45\text{hh}:\text{mm}$

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