This problem involves a simple calculation of ratios. We are given the total distance of a journey and the distance covered by one mode of transport. Our goal is to determine the ratio of the distances covered by the car and the bullock cart....
Steps to Solve
Here's a step-by-step guide to solve this problem:
- Calculate the distance covered by the bullock cart: Subtract the distance covered by the car from the total journey distance.
Distance covered by bullock cart = Total distance - Distance covered by car
Distance covered by bullock cart = 100 km - 64 km = 36 km
- Form the ratio: Write the ratio of the distance covered by the car to the distance covered by the bullock cart.
Ratio = Distance covered by car : Distance covered by bullock cart
Ratio = 64 km : 36 km
- Simplify the ratio: Find the greatest common factor (GCD) of the two numbers and divide both sides of the ratio by the GCD.
GCD of 64 and 36 is 4
Simplified ratio = (64/4) : (36/4) = 16 : 9
The Solution
Therefore, the ratio of the lengths of journey covered by the car and bullock cart is 16:9. This means for every 16 km traveled by the car, the bullock cart covers 9 km.
Key Concepts
This problem utilizes the following key mathematical concepts:
- Ratio: A ratio compares two quantities of the same unit. It expresses how much of one quantity there is relative to the other.
- Greatest Common Factor (GCD): The largest number that divides two or more numbers without leaving a remainder.
- Simplification: Reducing a ratio to its simplest form by dividing both sides by their GCD.
Applications
Understanding ratios is essential in various fields such as:
- Mathematics: Ratios are fundamental in algebra, geometry, and trigonometry.
- Science: Ratios are used to express concentrations, proportions, and scales.
- Engineering: Ratios are used in designing structures, machines, and systems.
- Finance: Ratios are used to analyze financial statements and assess business performance.
Conclusion
By using simple arithmetic operations, we were able to determine the ratio of distances covered by the car and the bullock cart. This problem illustrates the importance of understanding ratios and their applications in various real-world scenarios.