*Or, $SD = 13$, and so from any of two original equations, we get, $SU = 5$.*Now only we explore the boat speed and the stream speed.

Furthermore, if distance is held constant, this relationship also means time and speed will be inversely proportional to each other.

We can believe this relationship from our every day experience also.

All time and distance sums at school level and that appear in competitive tests are based on these two sets of concepts.

We will take two problems on this topic area of time and distance just to highlight how problems can be solved in just a few simple steps by applying relevant problem solving techniques and strategies.

The actual act of using the representative variables is though a well-known mathematical technique of substitution.

To be able to use our problem solving resource in any domain we would prefer to call this instead the principle of representative, which is the core process and more abstract.On another occasion with the same speed it covers 35km upstream and 52km downstream in 11 hours. Problem analysis: Each of the two periods of 8 hours and 11 hours consists of two component time periods, one upstream at a speed that is the difference in boat speed and stream speed, and the other downstream at a speed that is a sum of boat speed and stream speed.Let us call the upstream speed of the boat as $SU$ and downstream speed $SD$.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.This is the first stage of use of Abstraction technique.Conventionally, the variables are straightaway assumed to be boat speed $B$ and stream speed $S$ and the equations are expressed in terms of these variables right from the start.Instead, if we move faster for the same duration we will cover a much larger distance.That is direct proportionality between distance and speed.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.

## Comments Distance Problem Solving

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