Worker A and worker B doing a project OK, so embarrassingly I've forgotten how to do this type of problem which I'll generalize:

$n$ workers of type $A$ can do a job in $x$ hours.  $m$ workers of type $B$ can do the same job in $y$ hours.  How long would it take $n_1$ workers of type $A$ and $m_1$ workers of type $B$ to do the job working together?

Logically I can see that $1$ type $A$ worker should spend $n$ times as much time as $n$ workers take.  Same with $B$. So a type $A$ worker can do the job in $nx$ hours and a type $B$ worker could do the job in $my$ hours.  I just don't seem to be able to figure out how long a mixture of type $A$ and type $B$ workers take.
Could someone please explain the process to me?  Thanks.

The rate of work of a worker from group $A$ is $\frac{1}{nx}$. The rate of a worker from group $B$ is $\frac{1}{my}$. Adding more workers from either group, you just add the rates. Now if you add up $m_1$ workers and $n_1$ workers from the groups you get a rate of 
$$n_1 \frac{1}{nx} + m_1\frac{1}{my}$$
And to get the time it takes, use 
$$\text{time} = \frac{1}{\text{rate}}$$
