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.

$nx$ man-hours of type A = $ym$ man-hours of type B
thus 1 man-hour of type B = $\dfrac{nx}{ym}$ man-hours of type A.
Convert to type A
so hours needed by given mix = $\dfrac{nx}{n_1 + \dfrac{nx}{ym}\cdot m_1}$ 
