(a) The work done against gravity is given by the potential energy formula:

\(W = mgh\)

where \(m = 600 \text{ kg}\), \(g = 9.8 \text{ m/s}^2\), and \(h = 15 \text{ m}\).

Thus, \(W = 600 \times 9.8 \times 15 = 90,000 \text{ J}\).

The total work done by the crane also includes the work done against resistance, which is 10,000 J. Therefore, the total work done is:

\(90,000 + 10,000 = 100,000 \text{ J}\).

(b) Given the average power \(P = 12.5 \text{ kW} = 12,500 \text{ W}\), we use the formula:

\(P = \frac{W}{t}\)

where \(W = 100,000 \text{ J}\).

Rearranging gives:

\(t = \frac{W}{P} = \frac{100,000}{12,500} = 8 \text{ s}\).