In three hours, manufacturer z can make b ball bearings. manufacturer y can make b ball bearings in 4 hours. manufacturer x can make b ball bearings in 6 hours. working together, how long will it take all three plants to make b ball bearings?

Each hour,

x makes b/6 bearings

y makes b/4 bearings

z makes b/3 bearings

Together, each hour, x, y and z together make

b/6+b/4+b/3=b (1/6+1/4+1/3) = b (2/12+3/12+4/12) = b (3/4) = 3b/4 bearings.

Time to make b bearings =

b / (3b/4) = 4/3 hours = 1 hour 20 minutes.