Math Problem Statement

Solve

Solve the provided practice problems, which involve various unit conversions and rate calculations.

Solution

Let’s solve the practice problems step by step.

1. Grace runs 3 miles a day. Find this rate in feet per day.

  • Conversion factor: 1 mile = 5280 feet.
  • Calculation:
    3miles/day×5280feet/mile=15,840feet/day.3 \, \text{miles/day} \times 5280 \, \text{feet/mile} = 15,840 \, \text{feet/day}.
  • Answer: Grace runs 15,840 feet/day.

2. Jeff drinks 10 cups of orange juice a day. Find this rate in pints per week.

  • Conversion factors: 1 pint = 2 cups, and 1 week = 7 days.
  • Calculation:
    10cups/day×1pint2cups×7days/week=35pints/week.10 \, \text{cups/day} \times \frac{1 \, \text{pint}}{2 \, \text{cups}} \times 7 \, \text{days/week} = 35 \, \text{pints/week}.
  • Answer: Jeff drinks 35 pints/week.

3. Jody runs the 500-yard dash for his school’s track team in 1 minute. Find this rate in yards per second.

  • Conversion factors: 1 minute = 60 seconds.
  • Calculation:
    500yards60seconds8.33yards/second\frac{500 \, \text{yards}}{60 \, \text{seconds}} \approx 8.33 \, \text{yards/second}.
  • Answer: Jody runs at approximately 8.33 yards/second.

4. Barry’s remote control car can move 5.5 feet in 1 second. Find this rate in miles per hour.

  • Conversion factors: 1 mile = 5280 feet, and 1 hour = 3600 seconds.
  • Calculation:
    5.5feet/second×3600seconds/hour5280feet/mile=3.75miles/hour.5.5 \, \text{feet/second} \times \frac{3600 \, \text{seconds/hour}}{5280 \, \text{feet/mile}} = 3.75 \, \text{miles/hour}.
  • Answer: The car moves at 3.75 miles/hour.

5. Some cheetahs can run as fast as 71 miles per hour. To the nearest hundredth, find this rate in feet per second.

  • Conversion factors: 1 mile = 5280 feet, and 1 hour = 3600 seconds.
  • Calculation:
    71miles/hour×5280feet/mile3600seconds/hour=104.13feet/second.71 \, \text{miles/hour} \times \frac{5280 \, \text{feet/mile}}{3600 \, \text{seconds/hour}} = 104.13 \, \text{feet/second}.
  • Answer: Cheetahs run at approximately 104.13 feet/second.

6. The world’s fastest bird is the peregrine falcon that flies up to 200 miles per hour. How fast is the peregrine falcon in feet per second?

  • Conversion factors: 1 mile = 5280 feet, and 1 hour = 3600 seconds.
  • Calculation:
    200miles/hour×5280feet/mile3600seconds/hour=293.33feet/second.200 \, \text{miles/hour} \times \frac{5280 \, \text{feet/mile}}{3600 \, \text{seconds/hour}} = 293.33 \, \text{feet/second}.
  • Answer: The peregrine falcon flies at 293.33 feet/second.

Let me know if you'd like detailed explanations for any of the problems or further clarifications!

Related Questions:

  1. How would you convert feet per second to miles per hour?
  2. If Grace doubled her daily running distance, how many feet per day would she run?
  3. How many yards does Jody run in 5 seconds at his current speed?
  4. What is the speed of a car moving at 10 miles per hour in feet per second?
  5. How long does it take a peregrine falcon to fly 1 mile at its top speed?

Tip:

When converting rates, always confirm your units match before multiplying or dividing. This prevents common errors in unit conversion!

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Math Problem Analysis

Mathematical Concepts

Unit conversions
Rates and ratios
Speed and distance calculations

Formulas

1 mile = 5280 feet
1 hour = 3600 seconds
Rate = Distance / Time

Theorems

Dimensional Analysis
Proportional Reasoning

Suitable Grade Level

Grades 6-8