Understanding the Problem
To find out how long it takes for a car to cover 68 1/3 km when it travels at a speed of 25 2/7 km per hour, we need to calculate the time taken using the formula:
- Time = Distance / Speed
Converting Mixed Numbers to Improper Fractions
Before we proceed, let's convert the mixed numbers into improper fractions for easier calculations.
- 25 2/7 = (25 * 7 + 2) / 7 = 177 / 7 km/h
- 68 1/3 = (68 * 3 + 1) / 3 = 205 / 3 km
Calculating Time
Now we can substitute these values into the time formula:
- Time = Distance / Speed
- Time = (205 / 3) / (177 / 7)
Multiplying by the Reciprocal
To divide by a fraction, we multiply by its reciprocal:
- Time = (205 / 3) * (7 / 177)
Performing the Multiplication
Now, we can simplify this calculation step by step:
- Time = (205 * 7) / (3 * 177)
- Time = 1435 / 531
Final Calculation
Now, we can convert this improper fraction into a mixed number to make it easier to understand:
- 1435 ÷ 531 ≈ 2.70 hours, which means approximately 2 hours and 42 minutes.
Conclusion
Thus, it takes the car about 2 hours and 42 minutes to cover 68 1/3 km at a speed of 25 2/7 km per hour.