Foundation Mathematics Unit 1

Foundation Mathematics Unit 1

Sample learning activity – travelling by taxi

Taxis are part of the combination of modes of public transport around cities and suburbs. One method of getting around is using a taxi, and various charges and fees apply, depending on the circumstances of travel. Current fees and charges can be accessed from www.taxi.vic.gov.au and in particular http://taxi.vic.gov.au/passengers/taxi-passengers/taxi-fares ).

Taxi fares are calculated with respect to the time the trip took place, distance travelled (when travelling above 21km per hour and/or the time taken (when travelling below 21km per hour). The corresponding formulas are:

Using the distance travelled method

fare = distance (in kilometres) ´ rate per kilometre + flagfall fee

Using the time taken method

fare = time taken (per minute) ´ rate per minute + flagfall fee

Where the flagfall fee is the minimum charge for hiring a taxi. It is payable regardless of how far travelled or the time taken.

Part 1

a. Patsy is using a taxi at 4pm on a Monday to travel from work to home a distance of 15 km. How much will this trip cost her in a car?

b. Jimmy is taking a taxi to the city at 2 am on a Saturday the distance into the city is 22 km. However, night traffic works have caused the traffic is moving under 21km/h so the driver is charging him for time rather than distance. The trip takes 2 hours, how much will this journeys cost him?

c. Daisy has flown into Melbourne airport from Sydney for one day. She wants to make the most of her trip by visiting two zoos; Werribee zoo and Healesville Sanctuary and decides to is travel by taxi. The distance between the airport and Werribee is 43 km. The distance between Werribee zoo and Healesville sanctuary is 107 km via city link (southern link). Healesville Sanctuary and back to Melbourne Airport 75 km. How much will the trip cost if she is charged a daily rate?

Part 2

For each of the following scenarios use a maps tool such as: https://www.freemaptools.com/measure-distance.htm to calculate distances and then use the relevant formula to calculate the corresponding taxi fare. When calculating the taxi fare relevant any tolls, fees and charges should be included. Assume speed hasn’t fallen below 21km/h for any extended period of time, and the trip is in the daytime.

In each case, use a fare estimator, for example: http://taxi.vic.gov.au/passengers/taxi-passengers/taxi-fares/taxi-fare-estimator to check your answers.

a. Melbourne City Baths, Swanston Street to Fitzroy Gardens, Wellington Parade

b. Southern Cross Station, Spencer Street to Northern Hospital, Cooper Street, Epping

c. Mercy Hospital For Women, Studley Road, Heidelberg to Flinders Street Station, Flinders Street

d. Eureka Skydeck 88, Riverside Quay to Frankston Reservoir, Frankston South

e. Melbourne Park Hyatt to Werribee open range zoo. If payment is by credit card, how much more will this cost?

f. Re-calculate each the above taxi fares using the overnight rate.

g. Construct a distance – time graph for one of these scenarios.

Part 3

a. Re-calculate the fare for each of the above scenarios using the time rate instead of distance method.

b. Which results a cheaper ride?

c. Why would a taxi driver calculate time take rather than distance?

d. Develop several scenarios related to the types of trips you and your friends might be likely to take, and calculate the corresponding fare using an appropriate method.

e. Construct a cost – time graph for one of these scenarios.

Areas of study

The following content from the areas of study is addressed through this learning activity.

Area of study / Content dot point
Patterns and number
Data
Measurement / 1, 2, 3, 4
1, 3
1, 5

Outcomes

The following outcomes, key knowledge and key skills are addressed through this learning activity.

Outcome / Key knowledge dot point / Key skill dot point
1 / Patterns and number
1, 2, 3, 4
Data
1, 3
Measurement
1, 3 / Patterns and number
1, 2, 3, 4, 5
Data
2
Measurement
1, 3
2 / 1, 2, 3 / 1, 2, 3, 4, 5
3 / 2, 3 / 1, 2, 3