A cyclist rides at an average speed of 18 mi per hour. If she wants to bike 212 km, how long (in hours) must she ride?
The Correct Answer and Explanation is:
To determine how long the cyclist must ride to cover 212 kilometers at an average speed of 18 miles per hour, we need to first convert the distance from kilometers to miles. This conversion is necessary because the speed is given in miles per hour.
The conversion factor between kilometers and miles is 1 kilometer = 0.621371 miles. So, to convert 212 kilometers to miles, we multiply: 212 km×0.621371=131.47 miles212 \text{ km} \times 0.621371 = 131.47 \text{ miles}212 km×0.621371=131.47 miles
Now that we know the cyclist needs to cover 131.47 miles, we can use the formula for time, which is: Time=DistanceSpeed\text{Time} = \frac{\text{Distance}}{\text{Speed}}Time=SpeedDistance
We already know the cyclist’s speed is 18 miles per hour, and the distance to be traveled is 131.47 miles. So, substituting these values into the formula: Time=131.47 miles18 miles per hour=7.3 hours\text{Time} = \frac{131.47 \text{ miles}}{18 \text{ miles per hour}} = 7.3 \text{ hours}Time=18 miles per hour131.47 miles=7.3 hours
Thus, the cyclist will need approximately 7.3 hours to complete the 212 kilometers.
Explanation
The key steps in this problem are:
- Conversion of units: Since the speed is in miles per hour, we first convert the distance from kilometers to miles using the appropriate conversion factor.
- Time calculation: Once the distance is converted to miles, we use the time formula. Time is calculated by dividing the distance by the speed. This gives the total time the cyclist will need to ride at the given speed to cover the distance.
This method ensures that the calculation accounts for both the distance to be traveled and the cyclist’s speed, leading to an accurate estimate of how long the ride will take.
