Train from Brno

The first train started from Brno at 8 AM at 60 km per hour. The second train started from Opava at 7 o'clock at 40 kilometers per hour. In how many hours and how far from cities do trains meet when the distance between cities is 200 kilometers?

Result

T = 9:36 h
b =  96 km
o =  104 km

Step-by-step explanation:

$$\begin{gathered} v_1=60\text{km/h} \\ {v}_2=40\text{km/h} \\ s=200\text{km} \\ b+o=s \\ b=v_1\cdot (t-8) \\ o=v_2\cdot (t-7) \\ {v}_1\cdot (t-8)+v_2\cdot (t-7)=s \\ 60\cdot (t-8)+40\cdot (t-7)=200 \\ 100t=960 \\ t=\frac{960}{100}=9.6 \\ t=\frac{48}{5}=9.6 \\ T=t=9.6=9:36\text{h} \end{gathered}$$

$b=v_1\cdot (t-8)=60\cdot (9.6-8)=96\text{km}$

$o=s-b=200-96=104\text{km}$

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