Question:
Broadway Cabs and City Cabs are two competing taxi services. Broadway Cabs cost $2.50 plus $2.60 per mile. City Cabs cost $4.00 plus $2.45 per mile.
1) Write a linear cost function for each company.
2) What length ride costs the same for both companies?
3) For rides longer than that, which company is cheaper and why?
Solution:
\( B = \) cost in $ of a ride with Broadway Cabs
\( C = \) cost in $ of a ride with City Cabs
\( m = \) length of ride in miles
\( B(m)= 2.50 + 2.60m \)
\( C(m) = 4.00 + 2.45m \)
\(B(m)=C(m) \)
\( 2.5+2.6m=4+2.45m \)
\( 0.15m=1.5\)
\( m = 10 \)miles
So a 10 mile ride costs the same for both companies
For rides longer that 10 miles, City Cab is cheaper because its per/mile rate is lower.
