Renting a Car


(Source: Adapted from Mathematics Teaching in the Middle School, May 1999).

A car rental agency charges $37.50 per day and $0.23 per mile or fraction thereof to rent a car. A bus ticket cost $85.75 round trip. Under what circumstances is each option more economical?

First, let me tell you about the trip Khari and I are planning to Miami. We plan on leaving Wednesday evening at about 11 p.m. We will drive roughly 12 hours...701.8 miles or 1129.4 kilometers (starting out at my house). We will make periodic stops along the way to stretch, fill up on gasoline, or get snacks. While we are in Miami, I predict we may travel an extra 300 miles in and around the Miami Beach area. We will leave Sunday morning at 2 a.m. to make the long trek back. So, this is a great way to map it out. Here are the directions (using MapQuest from an arbitrary point in Atlanta):



Atlanta - Miami Trip 2001

1: Start out going North on CAPITOL AVE SE/CAPITOL AVE SW towards MARTIN LUTHER KING JR DR SW by turning left.
0.0 miles
( 0.1 km)

0.1 miles
( 0.1 km)

0.5 miles
( 0.9 km)

0.2 miles
( 0.4 km)

5: Take the I-85 S/I-75 S ramp.
0.3 miles
( 0.5 km)

6: Merge onto I-75 S.
68.0 miles
( 109.4 km)

7: Take the I-475 S exit, exit number 177, towards VALDOSTA.
0.4 miles
( 0.7 km)

8: Merge onto I-475 S.
15.2 miles
( 24.4 km)

9: Take the I-75 S/GA-401 S exit.
0.2 miles
( 0.4 km)

10: Merge onto I-75 S.
300.5 miles
( 483.6 km)

11: Take the FLORIDA'S TURNPIKE SOUTH exit, exit number 65, on the left towards ORLANDO.
0.7 miles
( 1.1 km)

12: Merge onto FLORIDA'S TURNPIKE S (Portions toll).
265.1 miles
( 426.7 km)

13: FLORIDA'S TURNPIKE S becomes I-95 S.
9.2 miles
( 14.9 km)

14: Take the NW 8TH ST exit, exit number 5A, towards ORANGE BOWL.
0.1 miles
( 0.2 km)

15: Stay straight to go onto 5A.
0.2 miles
( 0.3 km)

16: Turn SLIGHT RIGHT onto ramp.
0.2 miles
( 0.3 km)

17: Merge onto NW 3RD CT.
0.2 miles
( 0.3 km)

18: Turn LEFT onto NW 5TH ST.
0.4 miles
( 0.6 km)

19: Turn RIGHT onto N MIAMI AVE.
0.4 miles
( 0.6 km)


11 hours, 12 minutes 662.0 miles ( 1065.4km)



What do you know about Miami?

Where to should we stay?

1. Brigham Gardens Guesthouse

2. Key West Bed and Breakfast

3. Mayfair House

4. Miccosukee Resort & Convention Center


Miami's Top Spots: Restaurants with high ratings by MapQuest members:

1. Thai House 2
2. Benihana of Tokyo
3. La Paloma
4. Toni's New Tokyo Cuisine & Sushi Bar
5. By Word of Mouth
6. Cafe Vico
7. Bistro Zinc
8. Half Shell Raw Bar
9. The Left Bank
10. Athena by the Sea

Attractions we are thinking of visiting:

1. Miami Seaquarium

2. Florida Everglades

3. Ocean Drive

4. Florida Keys

5. Biscayne National Park



Just to recap:

car rental agency charges $37.50 per day and $0.23 per mile to rent a car

bus ticket costs $85.75 round trip

Under what circumstances is each option more economical?


Some factors we may encounter as we make this excursion in a car versus making the trip by bus include, but is not limited to, the following:

1. How much gas will be used?

2. How much time will be spent...either by car or by bus? This factors into the situation because the amount of time (days) we have a rental will greatly affect the cost. With the bus, you must factor in bus delays or servicing at the time of departure...what happens if the bus breaks down....this will definitely cause delays and hamper the spirit of the trip.

3. You cannot introduce new variables into the given situation...such as what will you do once we reach Miami (if we take the bus) about transportation?

4. Where are we going once we reach Miami? What is the actual destination?

BUS - how will we get to our destination...hotel...etc. once we reach the bus station?

CAR - how much more driving will be done once we reach Miami? This will cause us to pay much more money if we drive all over town.

5. By far, the BUS is more economical than renting the car because if we think about the daily charges of the car rental agency plus the mileage, this will far exceed the round trip rate of the bus... Now, if we are talking about being thrifty...walking to different sites...maybe using the bus transportation system in Miami...or taxi service. If you are not used to walking everywhere, using public transportation, taxi service, this would be a headache and not worth saving the money. I am just the type of person to go site seeing in the car until I reach some place that I like...then maybe I will walk...but not for too long!!

6. Another factor that may also make the bus seem more economical: The fact that when renting a vehicle, one must puchase auto accidental insurance (or if this is an option, WHAT HAPPENS IF YOU GET INTO AN ACCIDENT???????...maybe your own auto insurance will go up if you do happen to get into an accident....more money out of your pocket!). If you get into an auto accident while riding the bus, you can...dare I say it...SUE the bus company!!

7. Here is the math to work out how the bus is really more economical ($ wise) for this trip:

car rental - 37.50 per day + .23 per mile

x = days

y = miles

37.50x + .23y = total cost

 Price per day

 Miles traveled round trip
 Total cost
 37.50 * 1 day = $37.50  .23 * 1704 mi = $391.92  $429.42
 37.50 * 2 days = $187.50  .23 * 1704 mi = $391.92  $579.42

Keep in mind that these totals DO NOT include gasoline!! There is really no need in calculating more numbers....they speak for themselves!