3: Distance Traveled

Simple Algorithm: Calculating Distance Traveled for a Car

• Objective: Develop a program to calculate the distance traveled by a car using the formula that relates distance, speed, and time.

Distance Formula

• The basic formula for calculating distance is:
  $\text{Distance} = \text{Speed} \times \text{Time}$

Step-by-Step Algorithm Development

Step 1: Initial Values Setup

• Define initial parameters:

  • Speed = 20 (example value)

  • Time = 10 (example value)

• Calculation:

  • Multiply the two values to determine distance:

  • Calculation performed:
    $20 \times 10 = 200 \text{ miles}$

• Correct output after re-evaluation:

  • Distance = 200 miles

Step 2: Documenting the Calculation Process

• Procedure:

  • Multiply 20 (speed) by 10 (time):

  • Resulting distance calculated as 200 miles.

Step 3: Generalization of Variables

• Generalizing Speed:

  • Replace the initial speed value (20) with a variable identifier:

  • New representation: Speed

  • Now, the formula can take any speed value.

• Generalizing Time:

  • Replace the initial time value (10) with a variable identifier:

  • New representation: Time

  • Having generalized both parameters, the formula can now accommodate any speed and time values.

Final Generalization

• The finalized distance formula to use is:
  $\text{Distance} = \text{Speed} \times \text{Time}$

Testing the Algorithm

• Test Case 1:

  • Input: Speed = 5, Time = 5

  • Calculation:

  • Multiply:
    $5 \times 5 = 25$

  • Expected Output: 25

  • Actual Output: 25 (success)

• Test Case 2:

  • Input: Speed = 30, Time = 40

  • Calculation:

  • Multiply:
    $30 \times 40 = 1200$

  • Expected Output: 1200

  • Actual Output: 1200 (success)

Conclusion

• The algorithm has been successfully established, verified, and tested using the distance formula. The formula allows for dynamic input of speed and time to calculate distance, affirming its utility in various scenarios.