How long will it take to excavate a trench that is 8 feet deep, 4 feet wide, and 100 feet long with a production rate of 40 BCY and an efficiency factor of 75%?

To determine the time it will take to excavate the trench, we first need to calculate the volume of the trench and then use the production rate adjusted for efficiency to find the total time required.

The volume of the trench can be calculated using the formula for the volume of a rectangular prism:

Volume = Depth × Width × Length

Substituting the given dimensions:

Volume = 8 feet × 4 feet × 100 feet = 3200 cubic feet.

Next, we need to convert this volume into bank cubic yards (BCY). There are 27 cubic feet in a cubic yard, so the conversion is as follows:

3200 cubic feet ÷ 27 = approximately 118.52 BCY.

Given a production rate of 40 BCY, we can now account for the efficiency factor. The efficiency factor of 75% implies that only 75% of the production rate is effectively utilized during the excavation.

So, the effective production rate is calculated as follows:

Effective Production Rate = 40 BCY × 0.75 = 30 BCY.

Now, to determine how long it will take to excavate the trench using the effective production rate, we can use the formula:

Time = Volume ÷ Effective