Granny Takes the Train

The sun is shining, and the summer holidays have just begun. Peter is on a 300-m-long train with his grandmother. When they boarded, the train’s fuel tank was empty, but now it is being filled. The filling takes an hour, in spite of the fact that the speed at which the fuel flows into the tank doubles every minute.

In the meantime, the grandmother tells Peter about the time, when she was 19 and had her first baby. Shortly after giving birth, she attended a lecture along with 99 other new mothers. She could clearly remember the fashion of the time. Of the 100 women, 85 had red handbags, 75 wore black shoes, 60 wore a floral dress, and 90 had opal rings. Everybody had at least three of those things.

Finally, the train sets in motion. The grandmother talks about her six children. They were born exactly four years apart, and now the youngest is 19. The train passes into a tunnel. The tunnel is 300 m long, but the train is moving fast – 300 m per minute – so they are soon back into the light. Shortly after, the train arrives at the terminal, and Peter follows his grandmother out onto the platform.

1

How much time passes from the front of the train enters the tunnel until the back exits?

2

How old is Peter's grandmother?

3

How many of the young women at the lecture had brought all four things?

4

How long does it take to fill half of the train's fuel tank?