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# [Smart Math] Time Speed Distance Problem 6

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

### 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?

1. 50.4
2. 48.4
3. 46.4
4. 45.4
5. 44.4

### The Usual Method

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 = $\frac{2ab}{a+b}$ where ‘1’ and ‘2’ are the two speeds of upward and downward journeys.

Hence, average speed in this case = $\frac{2\times 50\times 40}{50+40}=\frac{4000}{90}$ = 44.44 km/hr

(Ans: 5)

Estimated Time to arrive at the answer = 30 seconds.

### Using Technique

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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