# Distance Problem Solving

If our train moves at a higher speed we will reach our destination in lesser time, isn't it?That is inverse relationship between the speed and time, where the distance is same in both the journeys at different speeds.

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We select the second expression (it could have been the first expression as well) and transform it to, $\displaystyle\frac \displaystyle\frac\times = 11\times$.

Subtracting this equation from the first equation we get, $\displaystyle\frac\left(39 - \displaystyle\frac\right) = 8 - \displaystyle\frac$ Or, $\displaystyle\frac = \displaystyle\frac$.

To contrast this simplicity we will present the conventional approach that is mostly followed in many occasions that we are aware of.

A motorboat covers 25km upstream and 39km downstream by travelling at same speed for 8 hours.

But again, instead of evaluating $SU$ or $SD$ directly we will treat their inverses as the target variables.

This is a much simpler form of abstraction and substitution.

But we recognize the great principle of representative, Politicians and officers who need to meet large number of people always meet with the representatives.

In this principle lies practical wisdom about how things should done. The much more practical system that evolved is - the masses select a small group of representatives who presents the issues on behalf of the masses.

In Substitution technique, Finally we observe that in the process of using these representative variables, we transform the equations to a simpler form and in fact use another well known technique originated from mathematics, the Solution process: With this simple assumption we can form two expressions for two occasions: $\displaystyle\frac \displaystyle\frac = 8$, and $\displaystyle\frac \displaystyle\frac = 11$.

We know that we would be able to evaluate both $SU$ and $SD$ from these two linear equations.

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