one taxi charges 75 cents for the first quarter-mile and 15 cents for each additional quarter-mile. the second company charges $1.00 for the first quarter-mile and 10 cents for each additional quarter mile. What distance would produce the same fare for the two companies?
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To determine the distance that would produce the same fare for the two companies, we can set up an equation and solve for the distance.
For the first taxi company:
Fare = 0.75 (for the first quarter-mile) + 0.15x (for each additional quarter-mile)
For the second taxi company:
Fare = 1.00 (for the first quarter-mile) + 0.10x (for each additional quarter-mile)
To find the distance that would produce the same fare for both companies, we can set the equations equal to each other and solve for x:
0.75 + 0.15x = 1.00 + 0.10x
0.15x - 0.10x = 1.00 - 0.75
0.05x = 0.25
x = 0.25 / 0.05
x = 5
Therefore, a distance of 5 quarter-miles would produce the same fare for both taxi companies.
To determine the distance that would produce the same fare for the two companies, we need to set up an equation. Let's denote the distance by 'd' (in quarter-miles) and the fare for each company by 'F1' and 'F2' respectively.
For the first company:
F1 = 0.75 + 0.15(d-1)
For the second company:
F2 = 1.00 + 0.10(d-1)
The fares for both companies are calculated as follows:
- The first company charges 75 cents for the first quarter-mile, and then adds 15 cents for every additional quarter-mile.
- The second company charges $1.00 for the first quarter-mile and then adds 10 cents for every additional quarter-mile.
Now, we need to find the distance 'd' at which the fares are equal, so we set F1 = F2:
0.75 + 0.15(d-1) = 1.00 + 0.10(d-1)
Simplifying the equation:
0.15(d-1) - 0.10(d-1) = 1.00 - 0.75
0.05(d-1) = 0.25
Now, we can solve for 'd':
0.05(d-1) = 0.25
d-1 = 0.25 / 0.05
d-1 = 5
Adding 1 to both sides of the equation:
d = 6
Therefore, a distance of 6 quarter-miles would produce the same fare for both companies.