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This is a problem number 3 from TOMATO based on Calculating Average Speed.

**Problem: Calculating Average Speed.**

A boy walks from his home to school at 6 kmph. He walks back at 2 kmph. His average speed, in kmph is

(A) 3; (B) 4; (C) 5; (D) $\sqrt {12}$;

**Discussion: **

Suppose the distance from home to school is t km.

Time taken for home to school journey: $\frac {t}{6}$

Time taken for school to home journey: $\frac {t}{2}$

Hence average speed = $\frac {distance}{time} = \frac {2t}{\frac{t}{6} + \frac{t}{2}} = 3$

There fore average speed is 3 kmph.

Note that it is the harmonic mean of the two given speeds instead of arithmetic mean.

- What is this topic: Elementary Arithmetic
- What are some of the associated concepst: Harmonic Mean
- Where can learn these topics: Cheenta I.S.I. & C.M.I. course, discusses these topics in the ‘Number Theory’ module.
**Book Suggestion:**Arithmetic by K.C. Nag

Advanced Mathematical Science. Taught by olympians, researchers and true masters of the subject.

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