Check-questions:

K
  1. A clock shows 9:00 a.m.. Determine in how many minutes the minute hand will catch up with the hour hand.
  2. A problem already known and solved by the Greek land surveyor Heron (around 170-100 B.C.) said:
    Water flows out of four pipes into one big container that would be filled by the first pipe only within one day, by only the second pipe within two days, by only the third pipe within three days and by only the fourth pipe within four days. How long would it take to fill the container if water is flowing through all four pipes at once?
  3. Two friends from one and the same town are supposed to get to another nearby city. The first walks and needs one hour for the distance. The other takes his bike and needs only 20 minutes. How long does it take the one by bike to catch up with the one walking, who is 15 minutes before him?
  4. Workers agree on getting 48fr per workday whereas they also agree on paying back 12fr for each day that they do not work. After 30 days they realize that they did not make any money. How many days did they work?
    This problem was given by the french mathematician Etienne Bezout (1730-1783).
  5. A worker needs 4 h more for completing an aggregate, another worker needs 9h more than, if they would both finish it together.
    How much time does each of them need to finish the aggregate by himself?
  6. A train goes past an on-watcher in 8 seconds and on a track that is 400 m long in 33 sec. Assess the trains length and speed.
  7. Assess the depth of a well when a stone dropped is heard after 4 seconds.
  8. A father is three times as old as his son. 12 years ago the father was 9 times as old as his son. How old are father and son today?
  9. Friedrich is 72 years old. He is one and a half times the age of the age Erwin used to be, when Friedrich was as old as Erwin is today.
    How old is Erwin?
  10. If grass seeds of two different kinds were mixed kind one of 8kg and kind two of 12 kg that mix costs 7,60Ç per 1kg. If reversed, 12kg of kind one and 8kg of kind two are mixed the mixture costs 8,40Ç per kg. How much is one kg of each kind?

Reflexion problems

  1. Give appropriate impulse questions and one problem sample for each, for which you will need to remember the division principle, the invariance principle and the extremum principle.
  2. Come up with a model of problem solving for yourself with rules and hints that you consider useful and not always self-evident. For easy retention, list no more than 5! Try to include some meaningful heuristics, but only those you consider essential. The problem solving model may be restricted to a particular topic such as problems of geometry of analysis...