one taxi cab company charges 75 cents for the first quarter mile and 15 cents for each additional quarter mile. the competing taxi company charges 1.00 for the first quarter mile and 10 cents for each additional mile. what distance would produce the same fare for the two taxi companies
75+15m=100+10m
solve for m
To determine the distance that would produce the same fare for the two taxi companies, we need to find the point where the two fare equations are equal. Let's denote the distance as x (in quarter miles).
For the first taxi company:
Fare = 0.75 + 0.15 * (x - 1) = 0.75 + 0.15x - 0.15 = 0.6 + 0.15x
For the second taxi company:
Fare = 1 + 0.10 * (x - 1) = 1 + 0.10x - 0.10 = 0.9 + 0.10x
Now, we can set these two equations equal to each other and solve for x:
0.6 + 0.15x = 0.9 + 0.10x
0.05x = 0.3
x = 0.3 / 0.05
x = 6
Therefore, a distance of 6 quarter miles would produce the same fare for both taxi companies.
To determine the distance that would produce the same fare for the two taxi companies, you need to set up an equation and solve for the unknown distance.
Let's assume the unknown distance is x (in quarter miles).
For the first taxi cab company, the fare is calculated as follows:
- First quarter mile = $0.75
- Additional quarter miles = (x - 1) * $0.15 = $0.15x - $0.15 (since the first quarter mile was already charged)
For the second taxi cab company, the fare is calculated as follows:
- First quarter mile = $1.00
- Additional quarter miles = (x - 1) * $0.10 = $0.10x - $0.10 (since the first quarter mile was already charged)
Now, we can set up the equation by equating the fares from the two companies:
$0.75 + $0.15x - $0.15 = $1.00 + $0.10x - $0.10
Simplifying the equation:
$0.15x - $0.15 = $0.10x + $0.90
Combining like terms:
$0.15x - $0.10x = $0.90 + $0.15
Simplifying further:
$0.05x = $1.05
Dividing both sides by $0.05:
x = $1.05 / $0.05
x = 21
Therefore, a distance of 21 quarter miles would produce the same fare for the two taxi companies.