Direct and inverse proportion

There is a truck traveling at $100$ km/h. It takes it $6$ h to do the distance that separates Barcelona from Madrid. How long will it take to do the same distance at $80$ km/h?

The most important thing of the exercise is to realize that it is an inverse proportion: the less velocity the more it will take to the truck to do the distance between both cities.

So, an inverse rule of three will be applied to solve it:

$$\begin{eqnarray} 6 \ \mbox{h} & \rightarrow & 100 \ \mbox{km/h}\\ x \ \mbox{h} & \rightarrow & 80 \ \mbox{km/h} \end{eqnarray}$$

We apply the rule of three for inverse proportions:

$\dfrac{6}{x}=\dfrac{80}{100} \Rightarrow 80x=6\cdot100 \Rightarrow 80x=600 \Rightarrow x=\dfrac{600}{80}=7,5$h

That is to say, it takes $1,5$ h more to go from Barcelona to Madrid if it slows down to $80$ km/h.

It will take $7,5$ h for the truck to do the same distance at $80$ km/h.

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