Victoria drove $21^1 / 2$ miles in $2 / 3$ of an hour. What was her speed?
A) $32^1 / 3$ miles per hour
B) $32^3 / 4$ miles per hour
C) $32^1 / 4$ miles per hour
D) $32^1 / 2$ miles per hour
Answer (2)
Convert the mixed number to an improper fraction: 21 2 1 = 2 43 .
Use the formula speed = distance / time.
Substitute the distance and time into the formula: speed = 3 2 2 43 = 4 129 .
Convert the improper fraction to a mixed number: 4 129 = 32 4 1 . The speed is 32 4 1 miles per hour.
Explanation
Understanding the Problem We are given that Victoria drove 21 2 1 miles in 3 2 of an hour. We need to find her speed in miles per hour.
Converting to Improper Fraction First, convert the mixed number 21 2 1 to an improper fraction: 21 2 1 = 2 21 × 2 + 1 = 2 42 + 1 = 2 43 So, Victoria drove 2 43 miles in 3 2 of an hour.
Stating the Formula The formula for speed is: speed = time distance In this case, the distance is 2 43 miles and the time is 3 2 hour.
Calculating the Speed Substitute the distance and time into the formula: speed = 3 2 2 43 = 2 43 ÷ 3 2 = 2 43 × 2 3 = 2 × 2 43 × 3 = 4 129 So, Victoria's speed is 4 129 miles per hour.
Converting to Mixed Number Now, convert the improper fraction 4 129 to a mixed number: 4 129 = 32 4 1 So, Victoria's speed is 32 4 1 miles per hour.
Final Answer Therefore, Victoria's speed was 32 4 1 miles per hour. The correct answer is C.
Examples
Understanding speed calculations is useful in everyday life. For example, if you are planning a road trip, you can use the distance and the speed limit to estimate how long it will take to reach your destination. Also, knowing how to calculate speed helps in understanding various transportation-related scenarios, like calculating the average speed of a train or an airplane. This knowledge is also fundamental in physics for understanding motion and kinematics.
Victoria drove at a speed of 32 and 1/4 miles per hour, which corresponds to option C. This was calculated by converting the mixed number distance to an improper fraction, using the speed formula, and simplifying to find the final answer. The process involved converting and calculating using basic operations with fractions.
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