Problems from Direct and inverse proportion

Development:

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:

$\begin{array}{rcl}6\text{h}& \to & 100\text{km/h}\\ x\text{h}& \to & 80\text{km/h}\end{array}$

We apply the rule of three for inverse proportions:

${\displaystyle \frac{6}{x}}={\displaystyle \frac{80}{100}}\Rightarrow 80x=6\cdot 100\Rightarrow 80x=600\Rightarrow x={\displaystyle \frac{600}{80}}=7,5$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.

Solution:

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

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