Question

Carletta and Johnathan are entrepreneurs making mother boards for computers that are being manufactured by their friend, Dewey Sasser. Carletta can make one mother board in 12 hours while it takes Johnathan 16 hours to make one mother board. Dewey suggested they could produce mother boards faster if they combined forces and worked together to build each mother board. What will be the time, in hours, that Carletta and Johnathan can build a mother board when working together? (Round your answer to the nearest hour.)

Answer 1

Carletta works at the rate
x = (1 board)/(12 hours) = 1/12 mb/hr

Johnathan works at the rate
y = (1 board)/(16 hours) = 1/16 mb/hr

The combined working rate is
1/12 + 1/16 = 7/48 = 0.1458 mb/hr

The time to build a mother board (mb) when working together is
(1 mb)/(0.1458 mb/hr) = 6.8587 hrs = 7 hours (nearest hour)

Answer: 7 hours