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# 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:Â

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:Â Elementary Arithmetic
• What are some of the associated concepst: Harmonic Mean
• Where can learn these topics:Â CheentaÂ I.S.I. & C.M.I. course, discusses these topics in the â€˜Number Theoryâ€™ module.
• Book Suggestion:Â Arithmetic by K.C. Nag

## By Dr. Ashani Dasgupta

Ph.D. in Mathematics, University of Wisconsin, Milwaukee, United States.

Research Interest: Geometric Group Theory, Relatively Hyperbolic Groups.

Founder, Cheenta

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