One company can build a machine in 2 weeks and another can b

One company can build a machine in 2 weeks and another can build it in 5 weeks. How long will it take the two companies to build the machine when they are working together?

Solution

The first company, in one week, can do 1/2 of the whole job.

The Second Company, in one week, can do 1/5 of the whole job.

When we add these together, we find out what both companies can do together in one week

½ + 1/5

=> (5+2)/10=>7/10

Together, the companies can do 7/10 of the work in one week.

The time for the entire job is represented by the reciprocal of what can be done in one week, so the total job can be done in...

10/7 => 1.43 weeks