# Problems from 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?

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### 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:

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

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.

### Solution:

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

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