How long will it take to excavate a trench that is 8 feet deep by 4 feet wide by 100 feet long if the hourly production rate is 40 BCY and the operator has an efficiency factor of 75%?

To determine how long it will take to excavate the trench, first, calculate the volume of the trench in bank cubic yards (BCY). The formula for calculating the volume of a rectangular prism is length × width × height.

The dimensions of the trench are:

• Depth: 8 feet

• Width: 4 feet

• Length: 100 feet

Converting dimensions from feet to yards (since 1 yard = 3 feet):

• Depth: 8 feet = 8 / 3 = 2.67 yards

• Width: 4 feet = 4 / 3 = 1.33 yards

• Length: 100 feet = 100 / 3 = 33.33 yards

Now, calculating the volume in cubic yards:

Volume = length × width × depth

Volume = 33.33 × 1.33 × 2.67 ≈ 117.78 cubic yards (BCY)

Next, consider the production rate and the efficiency factor. The hourly production rate is 40 BCY, but since the operator has an efficiency factor of 75%, the effective production rate is:

Effective production rate = actual rate × efficiency factor

Effective production rate = 40 BCY