Question

A and B can do a piece of work in 30 days ,while B and C can do the same work in 24 days and C and A in 20 days. if they all work together, in how many days will the work finish?

Answer 1

$(1 \div a) + (1 \div b) = 1 \div 30 \\ (1 \div b) + (1 \div c) = 1 \div 24 \\ (1 \div c) + (1 \div a) = 1 \div 20 \\ so \: that \: \\ (1 \div a) + (1 \div b) + (1 \div c) = 1 \div 16 \\ so \: they \: can \: work \: together \: in \: 16 \: days$