Where and when

The truck left Kremnica at 11:00 h at a speed of 60km/h. At 12:30 h, the passenger car started at an average speed of 80km/h. How many kilometers from Kremnica will the passenger car reach truck, and when?

Result

s =  360 km
T = 17:00 hh:mm

Solution:

$$\begin{gathered} s_1=s_2 \\ {v}_1=60\text{ km/h } \\ {v}_2=80\text{ km/h } \\ {v}_1\cdot (t-11.00)=v_2\cdot (t-(12+30\mathrm{/}60)) \\ 60\cdot (t-11.00)=80\cdot (t-(12+30\mathrm{/}60)) \\ 1200t=20400 \\ t=17 \\ s=v_1\cdot (t-11.00)=60\cdot (17-11.00)=360\text{ km } \\ \text{ Correctness test: } \\ {s}_2=v_2\cdot (t-12.50)=80\cdot (17-12.50)=360\text{ km } \\ {s}_1=s_2=s \end{gathered}$$

$T=t=17:00\text{ hh}:\text{mm}$

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