Prievidza–Brezno

Cyclist Juraj set out from Prievidza toward Brezno in the morning at 6:30 and traveled at an average speed of 18 km/h. He took a half-hour break along the way. At the same time, cyclist Peter set out from Brezno toward Prievidza along the same road at an average speed of 20 km/h and went without a break. The cyclists met. How many kilometers did Juraj ride to the meeting point?
(Prievidza–Brezno = 124 km)

Final Answer:

j =  54 km

Step-by-step explanation:

$$\begin{gathered} v_1=18\text{km/h} \\ {v}_2=20\text{km/h} \\ s=124\text{km} \\ j+p=s \\ j=v_1\cdot (t-1/2) \\ p=v_2\cdot t \\ {v}_1\cdot (t-1/2)+v_2\cdot t=s \\ 18\cdot (t-1/2)+20\cdot t=124 \\ 76t=266 \\ t=\frac{266}{76}=3.5 \\ t=\frac{7}{2}=3.5 \\ p=v_2\cdot t=20\cdot 3.5=70\text{km} \\ j=s-p=124-70=54\text{km} \end{gathered}$$

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