Average Speed Time and Distance

In this class, We discuss Average Speed Time and Distance.

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The reader should have prior knowledge of the speed and distance formula. Click Here.

Formula:

Suppose a man covers a certain distance at x km/hr and an equal distance at y km/hr.

Then the average speed during the journey is = (2xy)/(x+y)

I don’t remember the formula. It is very hard to remember all the formulas in aptitude.

How do we get the formula?

Try to understand the process of obtaining the formula.

The process helps in solving the bits.

The below diagram shows the journey.

He travelled D distance at x km/hr and another D distance in y km/hr.

Speed = Distance / Time

Time = Distance / Speed

t1 = D/x

t2 = D/y

S = distance / Time

S is average speed. The intuition why average speed? explained in the previous class

Distance = Total distance = 2D

Time = Total Time = t1 + t2

S = 2D / (D/x + D/y)

S = 2 / (1/x + 1/y)

S = 2xy / (x+y)

Similarly, the process is shown below if he traveled three equal distances with different speeds.

The below diagram shows the graphical understanding of the journey.

S = 3D / (D/x + D/y + D/z)

different distances are traveled at different speeds.

The below diagram and equation shows the complete understanding.

Average Speed = (D1 + D2)/ (D1/x + D2/y).