Math Problem Statement

The image lists several scenarios involving distances and times. Calculate the speed for each scenario using the formula: Speed = Distance/Time.

Solution

The image lists several scenarios involving distances and times. To solve for the speed in each case, we can use the formula for speed:

Speed=DistanceTime\text{Speed} = \frac{\text{Distance}}{\text{Time}}

Let's calculate the speed for each:

  1. (a) A car travels 60 miles in 2 hours: Speed=60 miles2 hours=30 miles per hour\text{Speed} = \frac{60 \text{ miles}}{2 \text{ hours}} = 30 \text{ miles per hour}

  2. (c) A cyclist travels 45 miles in 5 hours: Speed=45 miles5 hours=9 miles per hour\text{Speed} = \frac{45 \text{ miles}}{5 \text{ hours}} = 9 \text{ miles per hour}

  3. (e) A runner runs 100 meters in 10 seconds: Speed=100 meters10 seconds=10 meters per second\text{Speed} = \frac{100 \text{ meters}}{10 \text{ seconds}} = 10 \text{ meters per second}

  4. (g) A helicopter travels 425 miles in 5 hours: Speed=425 miles5 hours=85 miles per hour\text{Speed} = \frac{425 \text{ miles}}{5 \text{ hours}} = 85 \text{ miles per hour}

  5. (i) A dog runs 216 meters in 12 seconds: Speed=216 meters12 seconds=18 meters per second\text{Speed} = \frac{216 \text{ meters}}{12 \text{ seconds}} = 18 \text{ meters per second}

  6. (k) A bird flies 19 miles in 2 hours: Speed=19 miles2 hours=9.5 miles per hour\text{Speed} = \frac{19 \text{ miles}}{2 \text{ hours}} = 9.5 \text{ miles per hour}

Let me know if you'd like more details about any of these calculations!


Follow-up questions:

  1. How do we convert speeds from miles per hour to meters per second?
  2. What is the speed of the runner in kilometers per hour?
  3. How does speed differ between land and air vehicles based on the examples?
  4. Can we calculate the acceleration for the runner if we knew their initial speed?
  5. How does the time factor affect the speed across different examples?

Tip: Remember that 1 mile is equal to approximately 1,609.34 meters when converting between miles and meters.

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Math Problem Analysis

Mathematical Concepts

Speed Calculation
Unit Conversion

Formulas

Speed = Distance/Time

Theorems

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Suitable Grade Level

Grades 6-8