What is the total number of hours required to excavate a trench that is 1500 feet long, 8 feet deep, and 4 feet wide, based on a power hoe's excavation rate of 35 cubic yards per hour?

To determine the total number of hours required to excavate a trench that is 1500 feet long, 8 feet deep, and 4 feet wide, we first need to calculate the volume of the trench in cubic yards, as the excavation rate provided is in cubic yards per hour.

The volume of the trench can be calculated using the formula for the volume of a rectangular prism, which is length × width × height. In this case, we need to convert the dimensions from feet to yards since there are 3 feet in a yard:

1. Length: 1500 feet ÷ 3 = 500 yards

2. Depth: 8 feet ÷ 3 = approximately 2.67 yards

3. Width: 4 feet ÷ 3 = approximately 1.33 yards

Now, we can calculate the volume in cubic yards:

Volume = Length × Width × Depth

Volume = 500 yards × 1.33 yards × 2.67 yards ≈ 1,775 cubic yards

Next, we need to divide the total volume by the rate of excavation provided by the power hoe, which is 35 cubic yards per hour:

Total hours required = Total volume ÷ Excavation rate