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 and Johnathan can complete the work in 7 hours while working together.

Explanation:

Carletta can make one mother board in 12 hours.

Johnathan can make one mother board in 16 hours.

Let the time taken together to complete the work be t.

And together they are doing '1' work.

So, together they can complete the work in :

`(t)/(12)+(t)/(16)=1`

LCM of 12 and 16 is 48

So, equation becomes:

`(4t+3t)/(48) =1`

`(7t)/(48)=1`

`7t=48`

t = 6.857 hours

And to the nearest hour it is 7 hours.

Therefore, Carletta and Johnathan can complete the work in 7 hours while working together.

Answer 2

The overall rate can be calculate using the formula:

1/x + 1/y = 1/z

where x and y is the rate of each person while z is the overall time they can do the work. Therefore:

1/12 + 1/16 = 1/z

z = 6.86 hour

Rounding off to the nearest hour:

z = 7 hours

They can finish when working together in 7 hours.