Motion

From two different locations distant 232 km started against car and bus. The car started at 5:20 with average speed 64 km/h. Bus started at 7:30 with average speed 80 km/h.

When they meet?
How many kilometers went the bus?

Result

x (hh:mm) = 8:09
s₂ =  51.9 km

Solution:

$$\begin{gathered} \mathrm{\Delta }t=(7-5)+{\displaystyle \frac{1}{60}}\cdot (30-20)=2.17h \\ {s}_1+s_2=232 \\ {v}_1(t+\mathrm{\Delta }t)+v_{2}t=232 \\ t={\displaystyle \frac{232-64\cdot \mathrm{\Delta }t}{64+80}}=0.65h \\ x=5+{\displaystyle \frac{1}{60}}\cdot 20+t+\mathrm{\Delta }t=8.153 \\ x=8:09 \end{gathered}$$

$s_2=v_{2}t=80\cdot 0.65=51.9\text{ km}$

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