Refer to the following table of values for taxi fares in var

Refer to the following table of values for taxi fares in various cities. The term flag drop refers to the cost of the first portion of a mile that is included in the initial fare. Depending on the city, the included portion may be as little as 0.10 mile or as much as 1 mile.

1) Two passengers, one in New York City and the other in Atlanta, each hire a taxi. Assume each encounters 6 minutes of wait time during their rides.

(a) Write a system of equations to represent the total costs of hiring a taxi in each indicated city as functions of the number of additional miles traveled beyond the flag drop. (Let m represent the number of miles traveled beyond the flag drop. Let

N(m)

represent the total costs of hiring a taxi in New York and

A(m)

represent the total costs of hiring a taxi in Atlanta.)

2)
(b) Solve the system of equations using algebra. Verify your solution by graphing the system or by substituting your solution back into the original equations. (If an answer does not exist, enter DNE.)
(m, y) = (_____,______)

3) Choose the correct letter that correspond to the above question:

a) The taxi fare in both New York and Atlanta is $11.00 for a trip 2.95 miles beyond the flag drop (assuming six minutes of waiting time).

b) The taxi fare in both New York and Atlanta is $12.20 for a trip 3.7 miles beyond the flag drop (assuming six minutes of waiting time).   

c) It is not possible for a trip of any distance beyond the flag drop in New York City and Atlanta to have the same total fare (assuming six minutes of waiting time).

d) The taxi fare in both New York and Atlanta is $13.80 for a trip 3.95 miles beyond the flag drop (assuming six minutes of waiting time).

e) The taxi fare in both New York and Atlanta is $11.40 for a trip 4.7 miles beyond the flag drop (assuming six minutes of waiting time).

4)

(c) Explain what your answer in part means by picking a letter below and if it makes sense in the context of the problem:

a) The answer makes sense in the context of the problem.

b) The answer does not make sense in the context of the problem.   

Solution

1. (Let m represent the number of miles traveled beyond the flag drop. Let N(m) represent the total costs of hiring a taxi in New York and A(m) represent the total costs of hiring a taxi in Atlanta.)

N(m)   = 2.5+ 2 m + 0.4 x 6      Here each encounters 6 minutes of wait time during their rides.

          = 2.5+ 2 m + 2.4,

N(m) = 4.9 + 2 m,

A (m) = 2.5+ 2 m + 0.35 x 6      Here each encounters 6 minutes of wait time during their rides.

        = 2.5+ 2 m +2.1

A(m) = 4.6+ 2 m,

2. Substituting m = 0, in the equation of fares in New York

N(2) = 4.9 + 2 (0)

        = 4.9

(m, y) = (0, 4.9)

This is the cost of hreing a taxi in New York which waits for 6 minute and goes zero mile.