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?

Verified step by step guidance

1. Step 1: Convert the distance from kilometers to miles. Since 1 mile is approximately equal to 1.60934 kilometers, you can use this conversion factor to convert 212 kilometers to miles. The conversion can be done by dividing the distance in kilometers by the conversion factor.
2. Step 2: Once you have the distance in miles, you can calculate the time it would take to cover this distance at a speed of 18 miles per hour. The time taken (in hours) can be calculated by dividing the distance (in miles) by the speed (in miles per hour).
3. Step 3: Make sure to check your units. The distance should be in miles and the speed should be in miles per hour. The resulting time will be in hours.
4. Step 4: If your answer is a decimal, you may want to convert it to minutes for a more practical answer. To do this, multiply the decimal part by 60 (since there are 60 minutes in an hour).
5. Step 5: Always remember to round your final answer to a reasonable number of significant figures. In this case, since the given values are in whole numbers, your final answer should also be a whole number (or rounded to the nearest whole number).

Key Concepts

Unit Conversion

Unit conversion is the process of converting a quantity expressed in one unit to another unit. In this question, the cyclist's speed is given in miles per hour, while the distance to be traveled is in kilometers. To solve the problem, it is essential to convert either the speed to kilometers per hour or the distance to miles to ensure both measurements are in the same unit.

Speed, Distance, and Time Relationship

The relationship between speed, distance, and time is defined by the formula: Distance = Speed × Time. This fundamental concept allows us to calculate the time required to travel a certain distance at a given speed. Rearranging the formula to find time gives us Time = Distance / Speed, which is crucial for solving the cyclist's travel time.

Average Speed

Average speed is defined as the total distance traveled divided by the total time taken. It is a measure of how fast an object is moving over a specific distance. In this scenario, the cyclist's average speed of 18 miles per hour indicates the rate at which she can cover distance, which is necessary for determining how long it will take her to bike 212 kilometers.