Near Margaret's cabin is a 20-m water tower that attracts many birds during the summer months.

During a hot spell last year, the tower went dry, and Margaret had to have her water hauled in. She got lonesome without the birds visiting, so she decided to carry some water up the tower to attract them back. Her bucket has a mass of 10 kg and holds 30 kg of water when it is full. However, the bucket has a hole, and as Margaret climbed at a constant speed, water leaked out at a constant rate. Several birds took advantage of the shower below, but when she got to the top, only 10 kg of water remained for the birdbath.

(a) Write an expression for the mass of the bucket plus water as a function of the height y climbed.

(b) Find the work done by Margaret on the bucket.