1 1/2 miles of road. The crew can install 1/3 mile per day. How many days will it take to install the cable?
A. 5 days
B. 4 1/2 days
C. 3 days
D. 1/2 days
Answer (2)
Convert the mixed number to an improper fraction: 1 2 1 = 2 3 .
Divide the total road length by the installation rate: D = 3 1 2 3 .
Multiply by the reciprocal: D = 2 3 × 1 3 = 2 9 .
Convert to a mixed number: D = 4 2 1 . The final answer is 4 2 1 .
Explanation
Problem Analysis We need to determine how many days it will take a crew to install cable along a 1 2 1 mile stretch 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 3 So, the total road length is 2 3 miles.
Calculate Number of Days Let D be the number of days required to install the cable. We can set up the equation: D = Installation rate Total road length Substitute the values: D = 3 1 2 3 To divide by a fraction, we multiply by its reciprocal: D = 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 4 2 1 days to install the cable.
Final Answer The number of days required to install the cable is 4 2 1 days.
Examples
Imagine you're planning a cross-country road trip. If you know the total distance you want to travel and how far you can drive each day, you can use this type of calculation to estimate how many days the trip will take. For example, if you want to drive 1500 miles and you can drive 300 miles per day, it will take you 300 1500 = 5 days. This helps you plan your stops, accommodations, and overall schedule for the trip.
The crew will take 4 1/2 days to install the cable along 1 1/2 miles of road, as they can install 1/3 mile each day. The calculation involves converting the mixed number to an improper fraction and dividing it by the installation rate. Therefore, the answer is B. 4 1/2 days.
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