Height of a Pole

         What will be the height of a pole made up of all the millimeter cubes in one cubic metre, if placed one on top of another?

Answer:     You will be stunned at the answer. The pole would be 1000 kilometers high. Let us try to calculate it mentally.

A cubic metre equals: 1000 cubic millimeter x 1000 x 1000.

       One thousand millimeter cubes placed one atop another will make a pole 1 metre in height. And since we have 1000x 1000 times more cubes, we shall have a pole that is 1000 kilometers long.

The Problem of the Music Concert

         Recently I was at a music concert in Calcutta. I was sitting only one hundred feet away from the musicians.

           The performance was being broadcasted. My sister Vasantha who lives in Bangalore also heard the same concert on the radio. I am sure you know that Bangalore is over a thousand miles away from Calcutta, and also that travels at 1 100 feet per second. 

            Do you think there was any difference in the times at which the music was heard by Vasantha and myself? If so which one of us did hear the given note first?

Answer:   Yes, Vasantha did. The person listening to the radio hears the given note first.

A problem of Walking

                         Next door to me lives a man with his son. They both work in the same factory. I watch them going to work through my window. The father leaves for work ten minutes earlier than his son. One day lasted him about it and he told me’ he takes 30 minutes to walk to his factory, whereas his son is able to cover the distance in only 20 minutes.

                      I wondered, if the father were to leave the house 5 minutes earlier than his son, how soon the son would catch up with the father.

                       How can you find the answer?

Answer:   There are many ways of solving this problem without equations.¼

Here is one way: 

In five minutes the son covers ¼ of the way and the father ⅙ i.e. ¼ ─ ⅙ = ⅟₁₂ less than the son.

Since the father was ⅙ of the ahead of the son, the son would catch up with him after ⅙; ⁴⁄₁₂ = 2 five minute intervals, or 10 minutes.

There is one other way of doing this calculation which is even simpler: 

To get to work the farther needs 10 minutes more than the son. If he were to leave home 10 minutes earlier they would both arrive at work at the same time. If the father were to leave only five minutes earlier, the son would overhaul him half way to work i.e. 10 minutes later, since it takes him 20 minutes to cover the whole distance.