Calculating Total Distance Using Fractional Journeys
Understanding journey calculations and distance calculations is essential in various fields, from navigation and logistics to everyday planning. One common scenario involves calculating the total distance when a known fraction of the journey is given. This article provides step-by-step methods to calculate the total journey when 3/4 of it is known to be 16 km.
Method 1: Fractional calculation using subtraction
Given that 3/4 of the journey is 16 km, we can find the remaining 1/4 of the journey, which would be:
Journey still left in fraction 1 - 3/4 1/4
To find the total journey, we calculate the distance for the remaining 1/4 of the journey:
Journey still left in km 16 / (3/4) 16 * (4/3) 64/3 km ≈ 5.33 km
So, the total journey would be:
Total journey 16 km 5.33 km 21.33 km
Method 2: Using proportions and unitary method
If 3/4 of the journey is 16 km, we can find the total journey by first determining the distance of 1/4 of the journey. We can use the unitary method for this purpose:
3 units 16 km 1 unit 16/3 km Total journey 4 units 16 * 4/3 64/3 km ≈ 21.33 km
A simpler mental calculation shows that if 3 units represent 16 km, then 1 unit would be 16/3 km, and thus the total journey would be:
Total journey 4 * (16/3) 64/3 km ≈ 21.33 km
Method 3: Direct algebraic solution
Let the total journey be X km. Given that 3/4 of the journey is 16 km, we can set up the equation:
3X/4 16
Solving for X:
X 16 * 4/3 64/3 km ≈ 21.33 km
To find the remaining journey, we calculate:
Journey left X - 16 64/3 - 16 64/3 - 48/3 16/3 km ≈ 5.33 km
Conclusion
Through various methods of calculation, we have determined that the total journey is approximately 21.33 km. This can be verified by the methods mentioned above. Understanding these calculations enhances one's ability to solve similar problems and can be useful in both academic and real-world scenarios.