Calculating Average Speed | Tomato Problem 3

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.

Chatuspathi:

• 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