Brian 2

Brian and Jake left their homes 500 miles apart and drove straight toward each other. It took 4 hours for the two to meet if Jake's speed was 15 mph slower than Brian's. What was Brian's speed?

Correct answer:

v₁ =  70 mph

Step-by-step explanation:

$$\begin{gathered} s=500\text{mi} \\ t=4\text{h} \\ {s}_1+s_2=s \\ s=v\cdot t \\ {v}_1\cdot t+v_2\cdot t=s \\ {v}_2=v_1-15 \\ {v}_1\cdot 4+v_2\cdot 4=500 \\ {v}_2=v_1-15 \\ 4v_1+4v_2=500 \\ {v}_1-v_2=15 \\ Row2-\frac{1}{4}\cdot Row1\to Row2 \\ 4v_1+4v_2=500 \\ -2v_2=-110 \\ {v}_2=\frac{-110}{-2}=55 \\ {v}_1=\frac{500-4v_2}{4}=\frac{500-4\cdot 55}{4}=70=70\text{mph} \\ {v}_1=70 \\ {v}_2=55 \end{gathered}$$

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