In 35.0 s, a pump delivers 0.574 m3 of oil into barrels on a platform 25.5 m above the intake pipe. The oil's density is 0.820 g/cm3.

To find the work done by the pump, we need to calculate the gravitational potential energy of the oil that is lifted.

Work done = Change in potential energy

Potential energy = mgh

Here's how we can calculate it step by step:

Step 1: Convert the density to kilograms per cubic meter.

Density in kg/m^3 = density in g/cm^3 * 1000

Density in kg/m^3 = 0.820 g/cm^3 * 1000 = 820 kg/m^3

Step 2: Calculate the mass of the oil delivered.

Mass = density * volume

Mass = 820 kg/m^3 * 0.574 m^3 = 471.28 kg

Step 3: Calculate the change in potential energy.

Change in potential energy = mass * gravitational acceleration * change in height

Gravitational acceleration (g) = 9.8 m/s^2

Change in height = height of platform = 25.5 m

Change in potential energy = 471.28 kg * 9.8 m/s^2 * 25.5 m = 118,735.04 Joules

Therefore, the work done by the pump is 118,735.04 Joules.