Question

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?

Answer 1

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.