Cars meeting distance

The distance between cities A and B is 165 km. A truck traveled from city A to city B at a speed of 50 km/h. Fifteen minutes later, a passenger drove from city B to city A at 72 km/h. How far will the passenger car travel before the two cars meet?

Final Answer:

s =  90 km

Step-by-step explanation:

$$\begin{gathered} a=165\text{km} \\ {v}_1=50\text{km/h} \\ {v}_2=72\text{km/h} \\ m=15\text{min}\to \text{h}=15:60\text{h}=0.25\text{h} \\ {v}_1\cdot (t+m)+v_2\cdot t=a \\ 50\cdot (t+0.25)+72\cdot t=165 \\ 122t=152.5 \\ t=\frac{152.5}{122}=1.25 \\ t=\frac{5}{4}=1.25 \\ s=v_2\cdot t=72\cdot 1.25=90\text{km} \end{gathered}$$

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