# Distance Problem Solving

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

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As per our oringinal definition, upstream speed $SU$ is the difference of the two speeds whereas downstream speed $SD$ is the sum of the two speeds.

Summing up the two relative speeds we get, $SU SD = 13 5 = 18$ to be equivalent to twice the higher speed of the boat $B$.

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.

One object moving faster than another but in the same direction will pass the second object at a relative speed which is the difference between the two speeds.

But if the two objects move in opposite directions, their speed relative to each other will be the sum of the two speeds.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.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.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.So boat speed is 9 km/hr and the stream speed $S$ is 4km/hr. The use of In this conventional approach no substitution is used so that the initial expression will be, $\displaystyle\frac \displaystyle\frac = 8$, and $\displaystyle\frac \displaystyle\frac = 11$.We decide to eliminate $B S$ and multiply first equation by 4 and the second by 3 to get, $\displaystyle\frac \displaystyle\frac = 32$, and $\displaystyle\frac \displaystyle\frac = 33$.$Distance = Time\times$ This is the most basic relationship between these three elements.Conceptually this means, for a moving object distance is directly proportional to either speed or time, the other remaining constant.

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