Consider a group of 20 workers and a set of 40 tasks. Every worker can do 6 different tasks, and every task can be done by 3 different workers. Show that one can assign each task to a worker who can do it in such a way that every worker gets two tasks.

Water at the rate of 1 kg/s is forced through a tube with a 2.5 cm inner diameter. the inlet water temperature is 15°c, and the outlet water temperature is 50°c. the tube wall temperature is 14°c higher than the local water temperature all along the length of the tube. what is the length of the tube?