Friends' meeting

Two friends Krol from Katowice and Sigmund from Graz agreed that they would go to meet each other and meet in the Czech Republic. By motorway, the distance from Katowice to Graz is 570 km. Both friends left their homes at the same time. Because in Austria the motorways are better, Sigmund's average speed was 30 km/h higher than Krol's.

What was the average speed of both friends if they met after 180 minutes? How far from both cities did they meet?

Final Answer:

a =  330 km
b =  240 km
s =  110 km/h
k =  80 km/h

Step-by-step explanation:

$$\begin{gathered} t=180\text{min}\to \text{h}=180:60\text{h}=3\text{h} \\ h=570\text{km} \\ a+b=h \\ a=s\cdot t \\ b=k\cdot t \\ s=30+k \\ s\cdot t+k\cdot t=h \\ (30+k)\cdot t+k\cdot t=h \\ (30+k)\cdot 3+k\cdot 3=570 \\ 6k=480 \\ k=\frac{480}{6}=80 \\ k=80 \\ s=30+k=30+80=110\text{km/h} \\ a=s\cdot t=110\cdot 3=330\text{km} \end{gathered}$$

$b=k\cdot t=80\cdot 3=240\text{km}$

$s=110=110\text{km/h}$

$k=80=80\text{km/h}$

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