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 the trench, we first need to calculate the volume of the trench in cubic yards. The trench dimensions are 1500 feet long, 8 feet deep, and 4 feet wide.

First, we convert these measurements from feet to yards since the excavation rate is given in cubic yards per hour. There are 3 feet in a yard, so:

• Length in yards: 1500 feet ÷ 3 = 500 yards

• Depth in yards: 8 feet ÷ 3 ≈ 2.67 yards

• Width in yards: 4 feet ÷ 3 ≈ 1.33 yards

Now, we calculate the volume of the trench using the formula for the volume of a rectangular prism:

Volume = Length × Width × Depth

Volume = 500 yards × 1.33 yards × 2.67 yards

Volume ≈ 1775 cubic yards

Next, using the power hoe's excavation rate of 35 cubic yards per hour, we can calculate the total hours needed for excavation:

Total hours = Total volume ÷ Excavation rate

Total hours = 1775 cubic yards ÷ 35 cubic yards per hour