Wendy is taking a cab ride. The ride costs $1.20 for the first 0.5 km, and $0.90 for each additional 0.5 km. If the trip costs $12.00, how many kilometres was the cab ride?
1.20 + .90k = 12.00
Solve for k.
Let the number of km be k
cost = 1.2 + (2k - 1)(.9)
(2k-1)(.9) = 12-1.2
1.8k - .9 = 10.8
1.8k = 11.7
k = 6.5
The trip was 6.5 km
check: cost = 1.2 + (2*6.5 - 1)(.9) = 12
To determine the number of kilometres of the cab ride, we need to calculate how much distance was covered for the given cost.
Let's start by calculating the cost of the additional distance after the first 0.5 km. The additional cost for every 0.5 km is $0.90. So, the cost of the additional distance can be calculated using the formula:
Additional cost = Total cost - Cost of the first 0.5 km
In this case, the total cost is $12.00, and the cost of the first 0.5 km is $1.20. Therefore, the additional cost is:
Additional cost = $12.00 - $1.20 = $10.80
To find the additional distance covered, we need to divide the additional cost by the cost per 0.5 km:
Additional distance = Additional cost / Cost per 0.5 km
In this case, the cost per 0.5 km is $0.90. Therefore, the additional distance is:
Additional distance = $10.80 / $0.90 = 12
Now, we can find the total distance covered by adding the distance of the first 0.5 km and the additional distance:
Total distance = Distance of the first 0.5 km + Additional distance
Distance of the first 0.5 km is 0.5 km, and the additional distance is 12 km. Therefore, the total distance covered is:
Total distance = 0.5 km + 12 km = 12.5 km
Hence, the cab ride was 12.5 kilometres long.