Determine 23741

Adam and Eve live 20 km apart. They are going to a meeting. Adam moves at a speed of 2 km/h faster than Eva. They will meet in one and a half hours. Determine their speeds.

Correct answer:

v₁ =  7.6667 km/h
v₂ =  5.6667 km/h

Step-by-step explanation:

$$\begin{gathered} t=1.5\text{h} \\ s=20\text{km} \\ {v}_1\cdot t+v_2\cdot t=s \\ {v}_1=2+v_2 \\ {v}_1\cdot 1.5+v_2\cdot 1.5=20 \\ {v}_1=2+v_2 \\ 1.5v_1+1.5v_2=20 \\ {v}_1-v_2=2 \\ Row2-\frac{1}{1.5}\cdot Row1\to Row2 \\ 1.5v_1+1.5v_2=20 \\ -2v_2=-11.33 \\ {v}_2=\frac{-11.33333333}{-2}=5.66666667 \\ {v}_1=\frac{20-1.5v_2}{1.5}=\frac{20-1.5\cdot 5.66666667}{1.5}=7.66666667 \\ {v}_1=\frac{23}{3}\doteq 7.666667 \\ {v}_2=\frac{17}{3}\doteq 5.666667 \end{gathered}$$

$v_2=5.6667=5.6667\text{km/h}$

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