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Understanding Rates: Converting Units and Calculating Speed

This chapter provides exercises on applying rates, focusing on unit conversions and speed calculations. It covers practical examples, such as converting time from days to hours and seconds to minutes, as well as calculating distances in different units. The chapter also discusses rates and unit rates in context, including real-world applications like traffic safety and space travel. Readers will learn how to estimate rates of change in altitude and convert measurements relating to famous landmarks and events, empowering them with essential mathematical skills.

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Understanding Rates: Converting Units and Calculating Speed

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  1. Applying Rates Chapter 3

  2. Warm-Up • 32 days = ______ hours • 1 second = ______ minute • 7 yards = ______ inches • Write the given fraction in simplest form.

  3. A rate is a ratio that compares two units.120 miles in 2 hours • A unit rate is a rate per one given unit.60 miles per hour

  4. Suppose a spacecraft leaves Earth at an average rate of 0.225 km/s. Express its rate of ascent in kilometers per minute.

  5. Highway traffic and safety engineers have some general guidelines they have developed over the years and hold now as standards. • If you are moving at 44 ft/s, it will take a minimum of 109 feet to stop your car in an emergency. • How many miles per hour is 44 ft/s?

  6. Highway traffic and safety engineers have some general guidelines they have developed over the years and hold now as standards. • If you are moving at 88 ft/s, it will take a minimum of 304 feet to stop your car in an emergency. • How many miles per hour is 88 ft/s?

  7. During its first ten minutes of flight, the Concorde climbs from ground level to the altitude shown by point B on the graph. Estimate the Concorde’s rate of change in altitude during this time period.

  8. The graph shows how the altitude of a hot air balloon changes during a 15-minute test flight. • Estimate the balloon’s rate of change in altitude during this time.

  9. Mt. Everest • Mt. Everest is 29,035 ft high. How many miles is this?

  10. Speed of Light • The speed of light is approximately 186,282.397 miles per second. What is the speed of light in miles per hour?

  11. Lance Armstrong • For his third win, Lance Armstrong won the Tour by covering 3,462 km at an average speed of more than forty km/hr—the third-fastest time in the history of the event. How far is 3,462 km in miles? 1 mi = 1.609344 km

  12. Lance Armstrong • For his third win, Lance Armstrong won the Tour by covering 3,462 km at an average speed of more than forty km/hr—the third-fastest time in the history of the event. How fast is 40 km/h in mph? 1 mi = 1.609344 km

  13. Coquihalla Highway • The speed limit on the Coquihalla Highway in British Columbia is 110 km/h. What is the equivalent speed in units of mi/h, rounded down to the nearest multiple of 5? 1 mi = 1.609344 km

  14. Homework

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