Sharing a Cab Activity

Prepared by:

Joseph Malkevitch
Department of Mathematics
York College (CUNY)
Jamaica, New York 11451


web page:

The information below is the "official" information about rates for meter taxis in NYC from the web page of the NYC (New York City) Taxi & Limousine Commission:

Metered Fare Information

Onscreen rate is ‘Rate #01 – Standard City Rate.’
The initial charge is $2.50.
Plus 50 cents per 1/5 mile or 50 cents per 60 seconds in slow traffic or when the vehicle is stopped.
In moving traffic on Manhattan streets, the meter should “click” approximately every four downtown blocks, or one block going cross-town (East-West).
There is a 50-cent MTA State Surcharge for all trips that end in New York City or Nassau, Suffolk, Westchester, Rockland, Dutchess, Orange or Putnam Counties.
There is a 30-cent Improvement Surcharge.
There is a daily 50-cent surcharge from 8pm to 6am.
There is a $1 surcharge from 4pm to 8pm on weekdays, excluding holidays.
Passengers must pay all bridge and tunnel tolls.
Your receipt will show your total fare including tolls. Please take your receipt.
The driver is not required to accept bills over $20.
Please tip your driver for safety and good service.
There are no charges for extra passengers or bags.

Toll Information

The passenger is responsible for paying all bridge and tunnel tolls.
Use of E-ZPass
A driver must use an E-ZPass when taking a toll bridge or tunnel and must pass the discounted toll amount to the passenger. The amount of the toll will be added to the metered fare at the end of the trip.
Round-trip tolls
Passengers must pay all tolls to and from the destination in Westchester and Nassau Counties.
Passengers must pay return tolls for trips over the Cross Bay Veterans, and Marine Parkway-Gil Hodges Memorial Bridges.
Passengers must pay for all tolls to and from Newark Airport.

You and a friend enter a cab but are not going to the same destination. You will be paying the bill when you leave the cab after your friend has already exited the cab. You and your friend have agreed that you should share the cost including a reasonable tip for the cab driver in a fair manner.

Question 1:

Develop a mathematical model for two people to fairly share the cost of a cab when they get off at different places. You can assume that an agreement about how to tip is decided on in advance of the trip and that the total bill will be settled with the cab driver at the end of the trip. You can also assume that a receipt for the trip will be available, and you will settle with your friend when you see her/him again. What information beyond the final fare and the information above might you need?

Question 2:

How would the situation change if there were a. more than two people involved? b. Each person settles what to pay when they leave the cab?