Motion 2

At 10 o'clock started car from place A at speed at 90 km/h, twenty minutes after starting another car from place B at a 60 km/h speed. The distance between places A and B is 120 kilometers. What time and where do they meet?

Result

T = 10:56 h
x =  84 km

Step-by-step explanation:

$$\begin{gathered} v_1=90\text{km/h} \\ {v}_2=60\text{km/h} \\ s=120\text{km} \\ {t}_1=10.00\text{h} \\ {t}_2=t_1+20/60=10+20/60=\frac{31}{3}\doteq 10.3333\text{h} \\ {v}_1\cdot (t-t_1)+v_2\cdot (t-t_2)=s \\ 90\cdot (t-10)+60\cdot (t-10.333333333333)=120 \\ 150t=1640 \\ t=\frac{1640}{150}=10.93333333 \\ t=\frac{164}{15}\doteq 10.933333 \\ T=t=10.9333=10.93333=10:56\text{h} \end{gathered}$$

$x=v_1\cdot (t-t_1)=90\cdot (10.9333-10)=84\text{km}$

Try another example