Okay, here are the steps to solve this problem:
a) Compute the required volume of borrow pit excavation:
Given: Net embankment volume = 257,000 cy
Unit weight of borrow material (loose) = 129 pcf
unit weight of compacted embankment = 114 pcf
Step 1) Convert 257,000 cy to cubic ft: 257,000 cy * 27 ft^3/cy = 6,989,000 ft^3
Step 2) Compute loose volume required: 6,989,000 ft^3 / (129 pcf - 114 pcf) = 123,890,000 ft^3 (or 287,480 cy)
Therefore, the required volume of borrow pit excavation is 287,480 cy.
b) Determine how many trucks will be required to complete the job:
Given: Truck capacity = 35,000 lbs
Unit weight of borrow material (compacted) = 114 pcf = 1,752 lbs/cy
Step 1) Convert 287,480 cy to tons: 287,480 cy * 1 ton / 27 cu yd = 10,626 tons
Step 2) Number of trucks = 10,626 tons / 35,000 lbs per truck = 304 trucks
Therefore, 304 trucks will be required to complete the job.
c) Determine how many gallons of water is needed to add to each truck:
Given: Moisture content required = 18.3%
Moisture content of borrow material = 16.5%
Unit weight of borrow material (compacted) = 1,752 lbs/cy
Step 1) Additional moisture needed = 18.3% - 16.5% = 1.8%
Step 2) Additional moisture per cu yd = 1.8% * 27 cu ft/cy * 62.4 lb/(ft^3*%) = 4.62 lbs/cy
Step 3) Additional moisture per truck (35,000 lbs capacity) = 35,000 lbs / 1,752 lbs/cy = 20 cy
Step 4) Additional moisture per truck = 20 cy * 4.62 lbs/cy = 93 lbs
Step 5) Convert 93 lbs to gallons (1 gal = 8.36 lbs): 93 lbs / 8.36 lbs/gal = 11.2 gallons
Therefore, 11.2 gallons of water is needed to add to each truck.
Let me know if you have any other questions!