Two cars

From A town started two cars to town B. The first begins at 7:00 at an average speed of 60 km per hour. The second car starts at 10:00 at an average speed of 100 km per hour. The first car will not stay in B, and on the way back, meet the second car halfway from A to B. At what time will they meet in hours?

Result

t = 10:45 h

Step-by-step explanation:

$$\begin{gathered} v_1=60\text{km/h} \\ {v}_2=100\text{km/h} \\ 1.5s=v_1\cdot (t-7) \\ 0.5s=v_2\cdot (t-10) \\ 1.5s=60\cdot (t-7) \\ 0.5s=100\cdot (t-10) \\ 1.5\cdot s=60\cdot (t-7) \\ 0.5\cdot s=100\cdot (t-10) \\ 1.5s-60t=-420 \\ 0.5s-100t=-1000 \\ Row2-\frac{0.5}{1.5}\cdot Row1\to Row2 \\ -80t=-860 \\ t=\frac{-860}{-80}=10.75 \\ s=\frac{-420+60t}{1.5}=\frac{-420+60\cdot 10.75}{1.5}=150 \\ s=150 \\ t=\frac{43}{4}=10.75=10:45\text{h} \end{gathered}$$

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