One taxicab charges 75 cents for the first quarter-mile and 15 cents for each additional mile. The competing taxi company charges $1.00 for the first quarter-mile and 10 cents for each additional mile.
1. what distance would produce the same fare for the two taxi companies?
2. How did you get the answer/
Assistance needed.
To find the distance that would produce the same fare for the two taxi companies, we need to set up an equation and solve for the distance.
Let's denote the distance in miles as 'd'. For the first taxicab, the fare can be expressed as 75 cents (or $0.75) for the first quarter-mile and 15 cents (or $0.15) for each additional mile. So the total fare for the first taxicab is:
Fare1 = $0.75 + $0.15 * (d - 0.25)
Similarly, for the second taxicab, the fare can be expressed as $1.00 for the first quarter-mile and 10 cents (or $0.10) for each additional mile. So the total fare for the second taxicab is:
Fare2 = $1.00 + $0.10 * (d - 0.25)
To find the distance that would produce the same fare for both taxicabs, we need to set Fare1 equal to Fare2 and solve for 'd':
$0.75 + $0.15 * (d - 0.25) = $1.00 + $0.10 * (d - 0.25)
Simplifying the equation, we get:
$0.15 * (d - 0.25) = $0.25 * (d - 0.25)
Now we can solve for 'd':
0.15d - 0.0375 = 0.25d - 0.0625
Rearranging the terms and combining like terms, we get:
0.1d = 0.025
Dividing both sides by 0.1, we find:
d = 0.025 / 0.1 = 0.25
So the distance that would produce the same fare for the two taxi companies is 0.25 miles.
To get this answer, we set up an equation by breaking down the fare for each taxicab based on the given rates and then equating them to find the distance 'd' at which both fares are equal. Finally, we solved the equation to find that the distance is 0.25 miles.