Louisa biked $50 \frac{4}{5}$ miles in 4 hours. How many miles did she bike per hour? Let $m$ represent the number of miles.
Answer (2)
Convert the mixed number 50 5 4 to an improper fraction: 5 254 .
Divide the total miles by the number of hours: 5 254 ÷ 4 = 5 254 × 4 1 = 20 254 .
Simplify the fraction: 20 254 = 10 127 .
Convert to a decimal: 10 127 = 12.7 . Therefore, Louisa biked 12.7 miles per hour.
Explanation
Convert mixed number to improper fraction First, we need to determine the total number of miles Louisa biked. The problem states she biked 50 5 4 miles. To make calculations easier, let's convert this mixed number to an improper fraction.
Calculate improper fraction To convert 50 5 4 to an improper fraction, we multiply the whole number (50) by the denominator (5) and add the numerator (4). This gives us 50 × 5 + 4 = 250 + 4 = 254 . So, the improper fraction is 5 254 .
Divide total miles by number of hours Now, we need to find how many miles she biked per hour. Since she biked 5 254 miles in 4 hours, we divide the total miles by the number of hours to find the miles per hour. This is represented as 4 5 254 .
Multiply by the reciprocal To divide 5 254 by 4, we can rewrite 4 as 1 4 and then multiply by the reciprocal: 5 254 ÷ 1 4 = 5 254 × 4 1 = 20 254 .
Simplify the fraction Now, simplify the fraction 20 254 by dividing both the numerator and the denominator by their greatest common divisor, which is 2. So, 20 254 = 20 ÷ 2 254 ÷ 2 = 10 127 .
Convert to mixed number or decimal Finally, convert the improper fraction 10 127 to a mixed number or decimal. Dividing 127 by 10 gives us 12 with a remainder of 7. So, the mixed number is 12 10 7 , and the decimal is 12.7. Therefore, Louisa biked 12.7 miles per hour.
State the final answer The number of miles Louisa biked per hour is 12.7 miles.
Examples
Understanding rates, like miles per hour, is useful in many real-life situations. For example, if you are planning a road trip, you can use the miles per hour to estimate how long it will take to reach your destination. Similarly, if you are tracking your fitness progress while running or cycling, knowing your speed in miles per hour can help you monitor your improvement over time. This concept is also applicable in fields like logistics and transportation, where calculating delivery times and optimizing routes are crucial.
Louisa biked 12.7 miles per hour, calculated by converting the mixed number 50 5 4 miles to an improper fraction and then dividing by the total hours. This involved converting to the improper fraction 5 254 , dividing by 4 hours, simplifying the fraction to 10 127 , and converting to decimal form. The final answer is 12.7 miles per hour.
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