A car miles

A car begins heading along a path at 50 mph. A second car begins an hour later, along the same path traveling at 70 mph. For how long will the first car travel when the second car overtakes it?

Correct answer:

x =  175 mi

Step-by-step explanation:

$$\begin{gathered} v_1=50\text{mph} \\ {v}_2=70\text{mph} \\ T=1\text{h} \\ x=v_1\cdot t=v_2\cdot (t-T) \\ {v}_1\cdot t=v_2\cdot (t-T) \\ 50\cdot t=70\cdot (t-1) \\ 20t=70 \\ t=\frac{70}{20}=3.5 \\ t=\frac{7}{2}=3.5 \\ x=v_1\cdot t=50\cdot 3.5=175\text{mi} \end{gathered}$$

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