Math Problem Statement

Greg runs 9 miles in 82 minutes. How many miles does he run per minute? At Keller's Bike Rentals, it costs $19 to rent a bike for 5 hours. How many dollars does it cost per hour of bike use?

Solution

Let's solve the questions step by step:


(a) Greg runs 9 miles in 82 minutes. How many miles does he run per minute?

To calculate miles per minute, divide the total miles by the total minutes:

Miles per minute=Total milesTotal minutes=982\text{Miles per minute} = \frac{\text{Total miles}}{\text{Total minutes}} = \frac{9}{82}

Miles per minute=0.1098(rounded to 0.11 miles per minute)\text{Miles per minute} = 0.1098 \, \text{(rounded to 0.11 miles per minute)}


(b) Keller's Bike Rentals charges $19 to rent a bike for 5 hours. How many dollars does it cost per hour of bike use?

To calculate dollars per hour, divide the total cost by the total hours:

Dollars per hour=Total costTotal hours=195\text{Dollars per hour} = \frac{\text{Total cost}}{\text{Total hours}} = \frac{19}{5}

\text{Dollars per hour} = 3.8 \, \text{(rounded to $3.80 per hour)}


Final Answers:

(a) 0.11 miles per minute
(b) $3.80 per hour

Would you like further clarification or detailed steps?


Related Questions:

  1. How long would it take Greg to run 15 miles at the same rate?
  2. If the bike rental cost was $24 for 6 hours, how much would it cost per hour?
  3. How many miles can Greg run in 200 minutes at his current speed?
  4. What would be the total cost of renting a bike for 10 hours at Keller's Bike Rentals?
  5. If Greg increases his speed by 20%, how many miles would he run in 82 minutes?

Tip: For unit conversions or rates, always divide the total quantity by the total time or duration.

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Math Problem Analysis

Mathematical Concepts

Ratios and Rates
Division for Unit Conversion

Formulas

Miles per minute = Total miles / Total minutes
Dollars per hour = Total cost / Total hours

Theorems

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Suitable Grade Level

Grades 6-8