You can walk at a pace of [tex]$2 \frac{2}{3}$[/tex] miles per hour. At that pace, how long will it take you to walk [tex]$4 / 5$[/tex] of a mile?
A. [tex]$2 \frac{2}{15}$[/tex] hours
B. [tex]$1 / 20$[/tex] of an hour
C. [tex]$3 / 10$[/tex] of an hour
D. [tex]$3 \frac{1}{3}$[/tex] hours
Answer (2)
To walk 5 4 of a mile at a pace of 2 3 2 miles per hour takes 10 3 of an hour. This was calculated using the time formula Time = Speed Distance . The selected answer is option C: 10 3 of an hour.
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Convert the walking pace to an improper fraction: 2 3 2 = 3 8 miles per hour.
Use the formula: Time = Distance / Speed, where Distance = 5 4 mile and Speed = 3 8 miles per hour.
Substitute the values into the formula: Time = 5 4 / 3 8 = 5 4 × 8 3 = 40 12 .
Simplify the fraction to find the time in hours: Time = 10 3 hours. The final answer is 10 3 .
Explanation
Understanding the Problem We are given that you can walk at a pace of 2 3 2 miles per hour and we want to find out how long it will take to walk 5 4 of a mile at that pace.
Convert to Improper Fraction First, convert the walking pace to an improper fraction: 2 3 2 = 3 2 × 3 + 2 = 3 6 + 2 = 3 8 miles per hour.
Applying the Formula We know that Time = Distance / Speed. In this case, the distance is 5 4 miles and the speed is 3 8 miles per hour. So, Time = 5 4 / 3 8 .
Dividing Fractions To divide fractions, we multiply by the reciprocal: Time = 5 4 × 8 3 .
Multiplying Fractions Now, simplify the expression: Time = 5 × 8 4 × 3 = 40 12 .
Simplifying the Fraction Reduce the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 4: Time = 40 ÷ 4 12 ÷ 4 = 10 3 hours.
Final Answer Therefore, it will take 10 3 of an hour to walk 5 4 of a mile at a pace of 2 3 2 miles per hour.
Examples
Understanding how to calculate time, distance, and speed is useful in everyday life. For example, if you are planning a road trip, you can use this concept to estimate how long it will take to reach your destination. If you know the distance to your destination and the average speed you will be traveling, you can calculate the estimated travel time. This helps in planning your journey effectively, including when to take breaks and when you will arrive.
