Econocar offers two plans for one-week rentals of a compact car. A rate of $295 per week includes the first 1000 km. Extra distance costs 15 cents per kilometre. A weekly rate of $389 allows unlimited driving. Rounded to the nearest kilometre, beyond what driving distance is the unlimited driving plan cheaper?
295 + .15(k-1000) < 389
Solve for k.
To determine the driving distance beyond which the unlimited driving plan is cheaper, we need to compare the costs of both plans.
Let's break down the costs for each plan:
1. Plan 1: Rate of $295 per week, including the first 1000 km.
- If the total driving distance is 1000 km or less, the cost remains $295.
- If the total driving distance exceeds 1000 km, we need to consider the extra distance cost of $0.15 per kilometer.
2. Plan 2: Weekly rate of $389 for unlimited driving.
- With this plan, there are no additional charges for exceeding any distance limit.
Based on the given information, we need to find the driving distance where the cost of Plan 2 becomes less than or equal to the cost of Plan 1.
Let's assume the driving distance beyond which the unlimited driving plan is cheaper is represented by 'X' kilometers.
For Plan 1:
- The cost for the first 1000 km is $295.
- For any distance beyond 1000 km, the cost is $(0.15 × (X - 1000)).
For Plan 2:
- The cost is a fixed weekly rate of $389, regardless of the driving distance.
To find X, we need to equate the costs of both plans and solve for X:
295 + 0.15 × (X - 1000) = 389
Let's solve this equation:
295 + 0.15X - 0.15 × 1000 = 389
295 + 0.15X - 150 = 389
0.15X + 145 = 389
0.15X = 389 - 145
0.15X = 244
X = 244 / 0.15
X ≈ 1626.67
Rounding to the nearest kilometer, beyond a driving distance of 1627 kilometers, the unlimited driving plan becomes cheaper than Plan 1.