Artificial intelligent assistant

Linear Systems: Application Zoltan(who is behind Mali) and Mali are 18 km apart and begin to walk at the same time. If they walk in the same direction they meet after 6h. If they walk towards each other they meet in 2h. Find their speeds

Let $z$ be the speed of Zoltan, assumed constant, and let $m$ be the speed of Mali. Then $$6(z-m)=18 \qquad\text{and}\qquad 2(z+m)=18.\tag{1}$$ The first equation holds because the _rate of gain_ by Zoltan is $z-m$, and in $2$ hours, Zoli gains $18$ km. The second equation holds because when they are travelling toward each other, the distance between them is decreasing at $z+m$ km per hour.

From the two equations in (1), we find that $z-m=3$ and $z+m=9$. Add. We get $2z=12$, so $z=6$. Now we can find $m$.

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