Final answer:
The Polka Dot Cab Problem involves finding the linear relationship between cab fare and distance traveled. By comparing the cost and distance of two cab rides, the cost per mile is determined to be $0.95 and the base fare is $2.00.
Step-by-step explanation:
The question concerns a linear relationship between the distance traveled by cab and the fare cost. To solve the Polka Dot Cab Problem, we need to establish a formula that describes this linear relationship. Let's use the given information to find the cost per mile and the base fare.
Firstly, we know that Bob traveled 6 miles and paid $7.70, while Wally traveled 10 miles and paid $11.50. We can express these situations with two equations in the form of y = mx + b, where y is the total fare, m is the cost per mile, x is the distance traveled, and b is the base fare.
- For Bob: $7.70 = 6m + b
- For Wally: $11.50 = 10m + b
Subtracting the first equation from the second gives us $3.80 = 4m, or m = $0.95 per mile. Then we can substitute this value back into either equation to find the base fare. Let's use Bob's data:
- $7.70 = 6($0.95) + b
- b = $7.70 - $5.70
- b = $2.00 as the base fare
Thus, the cost of any cab ride with Polka Dot Cabs can be calculated using the formula Fare = $0.95 * distance + $2.00.