Brno-Tachov highway

The distance Brno-Tachov is 360 km. At 8:00 a. M. , a car travels from Brno on the highway, traveling at an average speed of 90 km/h. An hour later, a car leaves Tachov towards Brno, whose average speed is 110 km/h. Calculate how far apart they will be at 11:00 am, when the distance from Tachov-Plzeň is 60 km, Plzeň-Prague 100 km and Prague-Brno 200 km. Cars move only on this highway and against each other.

Correct result:

x =  130 km

Solution:

$$\begin{gathered} s=360\text{ km } \\ {v}_1=90\text{ km/h } \\ {v}_2=110\text{ km/h } \\ {t}_1=11.00-8.00=3\text{ h } \\ {t}_2=11.00-9.00=2\text{ h } \\ {s}_1=v_1\cdot t_1=90\cdot 3=270\text{ km } \\ {s}_2=v_2\cdot t_2=110\cdot 2=220\text{ km } \\ {s}_3=s_1+s_2=270+220=490\text{ km } \\ {s}_3>s \\ x=s_3-s=490-360=130\text{ km} \end{gathered}$$

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