A water distribution system with 3 switches A B and C is designed to transfer water from A to B The switches are connected together by 3 pipes These pipes are made of two different materials namely type I and II The failure rate of a pipe is proportional to its length and it also depends on the material The length of the pipes and their material types are shown on the diagram 7km I A 23km II Find the mean time to failure of the system B 19km I It is found that the failure rate per year per kilometre of type I and II pipes are 0 02t 2 3 and 0 008t 2 3 respectively where the unit of t is year Assume that the switches are perfectly reliable