Math Problem Statement

  1. If you are moving at a speed of 60 st mi/hr how fast are you moving in cm/sec? In ft/min

Solution

To convert a speed of 60 statute miles per hour (st mi/hr) into centimeters per second (cm/sec) and feet per minute (ft/min), we'll go step by step for both conversions.

Conversion from statute miles per hour to centimeters per second (cm/sec):

  1. Convert miles to kilometers:

    • 1 statute mile = 1.60934 kilometers
    • 60 miles = 60×1.60934=96.560460 \times 1.60934 = 96.5604 kilometers
  2. Convert kilometers to meters:

    • 1 kilometer = 1000 meters
    • 96.5604 km=96,560.4 meters96.5604 \text{ km} = 96,560.4 \text{ meters}
  3. Convert meters to centimeters:

    • 1 meter = 100 centimeters
    • 96,560.4 meters=9,656,040 centimeters96,560.4 \text{ meters} = 9,656,040 \text{ centimeters}
  4. Convert hours to seconds:

    • 1 hour = 3600 seconds
    • Speed in cm/sec = 9,656,040 cm3600 sec=2,682.23 cm/sec\frac{9,656,040 \text{ cm}}{3600 \text{ sec}} = 2,682.23 \text{ cm/sec}

So, 60 st mi/hr = 2,682.23 cm/sec.

Conversion from statute miles per hour to feet per minute (ft/min):

  1. Convert miles to feet:

    • 1 statute mile = 5280 feet
    • 60 miles=60×5280=316,800 feet60 \text{ miles} = 60 \times 5280 = 316,800 \text{ feet}
  2. Convert hours to minutes:

    • 1 hour = 60 minutes
    • Speed in ft/min = 316,800 feet60 min=5,280 ft/min\frac{316,800 \text{ feet}}{60 \text{ min}} = 5,280 \text{ ft/min}

So, 60 st mi/hr = 5,280 ft/min.


Final Answer:

  • 60 st mi/hr = 2,682.23 cm/sec
  • 60 st mi/hr = 5,280 ft/min

Do you want more details or have any questions?


Here are some related questions for further practice:

  1. How do you convert kilometers per hour to feet per second?
  2. What is the speed of light in miles per second?
  3. How do you convert meters per second to miles per hour?
  4. If a car is traveling 45 miles per hour, how fast is that in meters per second?
  5. How do you convert centimeters per second to miles per hour?

Tip: Always keep track of unit conversions systematically to avoid errors!

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Math Problem Analysis

Mathematical Concepts

Unit Conversion
Speed
Distance
Time

Formulas

1 mile = 1.60934 kilometers
1 kilometer = 1000 meters
1 meter = 100 centimeters
1 hour = 3600 seconds
1 mile = 5280 feet
1 hour = 60 minutes

Theorems

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Suitable Grade Level

Grades 8-10