Taxi rates are determined by local authorities. In city A, the night-time cost of a taxi includes a base fee of $3 plus a charge of $1.55 per kilometer. In city B, regardless of the time of day, the base fee is $2.70 with a charge of $1.87 per kilometer. For how many kilometers will cost of a night-time tact ride in each city be the same? Round to the nearest kilometer. What will the cost be in each city for the rounded number of kilometers?
To find the number of kilometers for which the cost of a nighttime taxi ride in each city is the same, we can set up the following equation:
3 + 1.55x = 2.70 + 1.87x
Simplifying the equation, we get:
0.32x = 0.70
Dividing both sides by 0.32, we find:
x = 2.1875
Rounding to the nearest kilometer, we get x = 2.
Therefore, the cost of a nighttime taxi ride in each city for 2 kilometers will be the same.
In City A, the cost will be:
Base fee: $3
Charge per kilometer: $1.55
Total cost = 3 + 1.55(2) = $3 + $3.10 = $6.10
In City B, the cost will be:
Base fee: $2.70
Charge per kilometer: $1.87
Total cost = 2.70 + 1.87(2) = $2.70 + $3.74 = $6.44
Therefore, for 2 kilometers, the cost in City A will be $6.10 and the cost in City B will be $6.44.