Imagine a situation that you take a taxi to go home. Some of your colleagues are together. Of course your houses are different from each other. But it is economical to share a taxi since the directions are the same.
Then, what is the best way to distribute fees for taxi?
This problem is frequently asked in real world. And I have also heard in elementary school class of mathematics such as below:
“Three persons, Mr. A, Mr. B and Mr. C are going to share a taxi to go home. The driveway is assumed to be straight. Mr. A’s home is 10km from here. Mr. B’s home is 10km from Mr. A’s home. Mr. C’s home is 10km from Mr. B’s home. Taxi fee is $10 every 10km. How much do each person must pay?”
The standard answer is that;
“Total cost for 30km driving is $30. This has to be distributed to 3 persons according to their riding distance. Mr. A rides in 10km, Mr. B 20km, and Mr. C 30km. So fair costs are, $5, $10, and $15, respectively.”
This answer is logically correct. But it is not practical. To adopt this method, we have to know the total fee in advance. It is not realistic.
So I recommend the second method.
The three persons share the taxi in first 10km. So the fee for this distance is to be distributed equally, $3.3 each other. And the second 10km are shared by Mr. B and Mr. C. Two must pay $5 each other. The last 10km is occupied by Mr. C. So he must pay $10 alone. After all, total fees of each person are, Mr. A $3.3, Mr. B $8.3, and Mr. C $18.3, respectively.
However, this method forces Mr. C to owe harder burden, compared to the previous one. It is not logically wrong but hardly acceptable for some people. If the driveway is not straight, the problem is more complicated. Mr. C must take longer time to go home than taking a taxi alone. It is much painful for him.
Indeed I usually pay the taxi fee a little much more than regulated for younger colleagues. It is not logical, but a social behavior.