In a large saucepan of boiling salted water, cook the beans until just tender, about 4 minutes. Using a slotted spoon, transfer the beans to a colander and refresh under cold running water. Drain and pat dry. Cut the beans into 2-inch lengths. Add the beets to the boiling water and simmer over moderate heat until tender, about 40 minutes; drain. Peel and cut them into 2-inch chunks.