Here’s and example of a **SMART MATH** problem for **TIME SPEED DISTANCE.**

**Problem**

**Problem**

A motorist travels to a place 100 kms away at an average speed of 50 km/hr and returns at 40 km/hr. The average speed of the journey is _________ km/hr?

- 50.4
- 48.4
- 46.4
- 45.4
- 44.4

**The Usual Method**

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Since, speed is a dependent variable on distance and time; we cannot directly find the Arithmetic Mean (Average) of the values.

Average speed of the journey is calculated using the Harmonic Mean concept:

Average speed = where ‘1’ and ‘2’ are the two speeds of upward and downward journeys.

Hence, average speed in this case = = 44.44 km/hr

**(Ans: 5)**

*Estimated Time to arrive at the answer = 30 seconds.*

**Using Technique**

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The Arithmetic Mean (AM) of the values 50 and 40 is 45.

We already know that the Harmonic Mean (HM) of a set of numbers is always less than the AM of the same set. (i.e. HM < AM).

Hence, the answer should be < 45. The only option < 45 is 44.4 km/hr

**(Ans: 5)**

*Estimated Time to arrive at the answer = 5 seconds.*

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