Question 156968
Solve the problem. Frank can type a report in 3 hours and James takes 4 hours. How long will it take the two of them typing together?

Let's make a table.

..........Rate of work.......Time worked.......Fractional Rate of Job Done

Frank.........1/3................x......................x/3

James.........1/4................x......................x/4

The number 1 will indicate the work they do together in the equation below.

x/3 + x/4 = 1

Solve for x.

Our LCD is 12.

Multiply 12 by every term on both sides of the equation.

Doing so, we now have this:

4x + 3x = 12

7x = 12

x = 12/7

The fraction 12/7 is about 1 hour and 70 minutes.

That's how long it will take both guys to do the job together.