Task

At Tauranga airport, there are three different taxi companies with taxis available for hire: Fred’s Taxi Company, P & G Taxis, and Flatrate Taxis.

Student Resource A gives the hire charge for each company and the distances to common destinations in Tauranga from the airport.

Represent the three taxi companies' charges using the same representation (for example, three equations or three graphs).

Recommend which taxi company to use for a trip to two of the common destinations.

Recommend distances for which it would be cheapest to use P & G Taxis.

Fred, who owns Fred’s Taxi Company, wants to be the cheapest taxi company people can use to travel to any destination. Describe at least two different ways Fred could realistically change his hire charges to achieve this goal. Include specific examples of the rates he could use.

Answer Template Fred’s Taxis - Fixed Charge $5.00 Per Km is $0.50

Equation of Graph: C = 0.5D +5 Gradient of Graph: Per Km is $0.50

P and G Taxis - Equation of Graph: Cost = 0.65D + 2 Fixed Charge: $2.00

Gradient of Graph: 0.65 / 65 cents per km FlatrateTaxis - $25 Flat fee up to 60km / additional after Fixed Charge: $25 Equation of Graph: C = $25 Gradient of Graph: 0

Answer Template – Find all three points of intersection Can be done after graphing Fred’s Taxis - Equation of Graph: Cost = 0.50D + 5 P and G Taxis - Equation of Graph: Cost = 0.65D + 2 FlatrateTaxis - Equation of Graph: Cost = $25 (to 60 km) Intersection of Freds Taxi and P and G

(20, 15)

Intersection of Fred and Flatrate

(40, 25)

Intersection of P and G and Flatrate

(35.38, 25)

Answer Template – Graph all three on same axes Fred’s Taxis - Equation of Graph: Cost = 0.50D + 5 P and G Taxis - Equation of Graph: Cost = 0.65D + 2 FlatrateTaxis - Equation of Graph: Cost = $25 (to 60 km)

Answer Template – Analyse Fred’s Taxi – Higher fixed cost than P and G ($5) but a lower per kilometre rate (gradient) of $0.50 per Km Fred’s taxi is the best option for trips from 20 to 40 kilometres P and G – Lowest fixed cost of all three ($2) but a higher per kilometre rate (gradient) of $0.65 per Km P and G is the best option for trips up to 20 kilometres Flatrate Taxi – Higher fixed cost of all ($25) but the lowest per km rate of all three Flatrate taxis are the best option for trips between 40 and 60 km (past 60 depends on the per km rate)

Answer Template – Analyse

FRED

13.50

17 27.50

P and G

13.05

17.60

31.25

Flatrate

25 25 25 Fred’s Taxi Costs City Centre = 0.5(17) + 5 = $13.50

Port = 0.5 (24) + 5 = $17.00

Bethlehem = 0.5 (45) + 5 = $27.50

P and G Taxi Costs City Centre = 0.65(17) + 2 = $13.05

Port = 0.65 (24) + 2 = $17.60

Bethlehem = 0.65 (45) + 2 = $31.25 Flatrate Taxi Costs City Centre = $25 Port = $25 Bethlehem = $25

Answer Template – Analyse

FRED

13.50

17 27.50

P and G

13.05

17.60

31.25

P and G Taxi is cheapest to the City Centre Fred’s Taxi is cheapest to the Port Fred’s Taxi is cheapest to Bethlehem

Flatrate

25 25 25

Answer Template – Two Destination Costs

FRED

13.50

17 27.50

P and G

13.05

17.60

31.25

Flatrate

25 25 25 City Centre and Port Fred = $30.50 P & G = $30.65

Flatrate = $50 City Centre and Bethlehem Fred = $41 P & G = $44.35

Flatrate = $50 Port and Bethlehem Fred = $44.50

P & G = $48.25

Flatrate = $50

Answer Template – Changes to Fred’s Costs

FRED

13.50

17 27.50

P and G

13.05

17.60

31.25

Flatrate

25 25 25 To be cheapest to all three destinations, Fred would need to change either his fixed cost, rate per km, or a combination of the two Fred is already the cheapest to all 3 pairs of destinations To be the cheapest for short distances, Fred would only need to lower his fixed cost by $0.50 which would make a trip to the City Centre $13.00 and cheaper than P and G To be lower to Bethlehem, Fred could change his fixed cost for trips of 45km and over to $2.

Answer Template – Changes to Fred’s Costs

FRED

13.50

17 27.50

P and G

13.05

17.60

31.25

Flatrate

25 25 25 The changes made to Fred’s fare schedule would only lose him $0.50 per ride up to 45km and would lose him $3 per ride for trips to Bethlehem. In order for him to be cheaper for all distances over 45km, he would need to make additional changes to stay below Flatrate taxis

NZQA Exemplar Excellence Answer