Math Problem Statement

 At a​ little-known vacation​ spot, taxi fares are a bargain. A 2828​-mile taxi ride takes 4242 minutes and costs ​$16.8016.80. You want to find the cost of a 3737​-minuteminute taxi ride. What unit price do you​ need?

Solution

To solve this problem, we need to determine the cost per minute of the taxi ride. Once we know the unit price (cost per minute), we can multiply it by the length of the desired taxi ride (37 minutes) to find the total cost.

Step 1: Determine the unit price (cost per minute).

We are given that a 42-minute taxi ride costs $16.80. To find the cost per minute, we divide the total cost by the number of minutes:

Unit price=16.8042=0.40 dollars per minute.\text{Unit price} = \frac{16.80}{42} = 0.40 \text{ dollars per minute.}

Step 2: Calculate the cost of a 37-minute taxi ride.

Now that we know the cost per minute is $0.40, we can calculate the total cost for a 37-minute ride by multiplying the unit price by 37:

Cost for 37 minutes=37×0.40=14.80 dollars.\text{Cost for 37 minutes} = 37 \times 0.40 = 14.80 \text{ dollars.}

So, the cost of a 37-minute taxi ride would be $14.80.

Would you like more details or have any questions about this solution?

Related Questions:

  1. What is the cost of a 50-minute taxi ride?
  2. How much would a 100-minute taxi ride cost at this rate?
  3. How would the cost change if the taxi rate increased by 10%?
  4. How long of a ride could you take with $25 at the current rate?
  5. If the taxi service charged a flat fee in addition to the per-minute rate, how would the formula change?

Tip:

Always remember to check if the problem requires a fixed base fee or any additional costs besides the per-minute charge.

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Math Problem Analysis

Mathematical Concepts

Unit Rate
Proportion
Basic Arithmetic

Formulas

Unit price = Total cost / Total time
Cost of ride = Unit price * Duration of ride

Theorems

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Suitable Grade Level

Grades 6-8