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.