Question

On a recent trip, I took a cab from the airport to my hotel. These were the cab fares posted on the door of the cab: $2.20 for the first 1⁄2 mile and 30 cents for each additional 1/5 mile. How far did I travel if my fare was $17.20? What would my fare be if I were to travel 16.8 miles? What would my fare be if I were to travel n miles? What kind of relationship is this? Justify your response and provide a visual representation (a graph) of the relationship.

Answer 1

We have the fixed cost of $2.20
For every mile travelled the fare is 5 × 30cents = $1.50

If the fare was $17.20, the number of miles travelled is $\frac{17.20-2.20}{1.50} = 10$ miles

The fare for travelling 16.8 miles is $2.20+1.5(16.8)= 27.40$

The fare for travelling n miles is $C=2.20+1.5n$

The relationship is a linear relationship as there is a constant increase of $1.50 for every mile travelled. The graph of the relationship is shown below