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I.S.I. and C.M.I. Entrance

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

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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