A crew has to install a cable beside $1 \frac{1}{2}$ miles of road. The crew can install $\frac{1}{3}$ mile per day. How many days will it take to install the cable?
A. 5 days
B. $4 \frac{1}{2}$ days
C. 3 days
D. $\frac{1}{2}$ days
Answer (1)
Convert the mixed number to an improper fraction: 1 2 1 = 2 3 .
Divide the total distance by the distance installed per day: 2 3 ÷ 3 1 = 2 9 .
Convert the improper fraction to a mixed number: 2 9 = 4 2 1 .
The crew will take 4 2 1 days to install the cable: 4 2 1 days .
Explanation
Problem Analysis We need to determine how many days it will take a crew to install a cable beside 1 2 1 miles of road, given that they can install 3 1 mile per day.
Convert to Improper Fraction First, convert the mixed number 1 2 1 to an improper fraction: 1 2 1 = 2 2 × 1 + 1 = 2 3 So, the crew needs to install a cable beside 2 3 miles of road.
Calculate Number of Days Next, divide the total distance by the distance the crew can install per day to find the number of days: 2 3 ÷ 3 1 = 2 3 × 1 3 = 2 × 1 3 × 3 = 2 9 Convert the improper fraction 2 9 to a mixed number: 2 9 = 4 2 1 Therefore, it will take the crew 4 2 1 days to install the cable.
Final Answer The number of days it will take to install the cable is 4 2 1 days.
Examples
Understanding rates and distances is crucial in many real-world scenarios. For instance, if you're planning a road trip, knowing your average speed (miles per hour) and the total distance helps you estimate the travel time. Similarly, in manufacturing, calculating production rates (units per day) helps determine how long it will take to fulfill an order. These calculations are also essential in project management, where estimating task durations is vital for meeting deadlines. In this case, we calculated the number of days required to install a cable, demonstrating a practical application of division and fractions in everyday planning and logistics.
