Final answer:
To determine if Angelique can build the entire fence in 5 hours, we need to calculate her rate of building the fence per hour. From the given information, after working for 2 5/6 hours, Angelique has completed 5/8 of the fence. To find her rate, divide the amount of fence completed by the number of hours worked: 5/8 ÷ 2 5/6. Therefore, Angelique cannot build the entire fence in 5 hours.
Step-by-step explanation:
To determine if Angelique can build the entire fence in 5 hours, we need to calculate her rate of building the fence per hour. From the given information, after working for 2 5/6 hours, Angelique has completed 5/8 of the fence. To find her rate, divide the amount of fence completed by the number of hours worked: 5/8 ÷ 2 5/6.
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction: 5/8 ÷ 2 5/6 = 5/8 x 6/17 = 30/136.
Therefore, Angelique completes 30/136 of the fence per hour. To find the total time it would take to complete the fence, we divide the remaining fraction of the fence (1 - 5/8) by her rate: 3/8 ÷ 30/136. Dividing fractions by fractions is the same as multiplying the first fraction by the reciprocal of the second fraction: 3/8 ÷ 30/136 = 3/8 x 136/30 = 4.08 hours.