Broadway Cabs and city cars are two competing taxi companies

Broadway Cabs and city cars are two competing taxi companies in a small town. The cost in dollars of Cab ride of d miles in C_1 = 2.9 + 3d for Broadway Cabs and C_2 = 4 + 2.89 d for city cars. Describe in words the fare breakdown for each company. How much does Broadway Cabs charges a flat rate? How much does Broadway Cabs charges per mile? How much does City Cars charges a flat rate? How much does City Cars charges per mile? Determine the conditions under which Broadway Cabs is cheaper than City cars. You need ride to the airport, which 12 miles from your house. To get the lowest fare, which is company should you call and how much will it cost?

Solution

C1 = 2.9 + 3d
C2 = 4 + 2.89d

a)
Broadway charges a flat fee of 2.9 dollars and a variable fee at
3 dollars per mile
City Cars charges a flat rate of 3 dollars and a variable fee at 2.89 dollars per mile

BC flat rate : 2.9 dollars

BC charge per mile : 3 dollars per mile

City Cabs flat rate : 4 dollars

City cabs charge per mile : 2.89 dollars per mile

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b)
BC cheaper than CC :

2.9 + 3d < 4 + 2.89d
3d - 2.89d < 4 - 2.9
0.11d < 1.1
d < 1.1/0.11
d < 10

So, BC is cheaper than CC when the distance traveled is less than 10 miles

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Since d = 12 miles,
CC will be cheaper

And the charge would be :
4 + 2.89*12
38.68 dollars ----> ANSWER