Working simultaneously at their respective constant rates, Machines A and B produce 800 nails in x hours. Working alone at its constant rate, Machine A produces 800 nails in r hours. In terms of x and r, how many hours does it take Machine B, working alone at its constant rate, to produce 800 nails?	Select the correct option.
A) x/(x+y)  B) y/(x+y)  C) xy/(x+y)  D) xy/(x-y)  E) xr/(r-x)
Pick some smart numbers for x and r.   Say x=1 hour and r=2 hours (notice that r must be greater than x, since the time for machine A to do the job, which is r hours, must be more than the time for machines A and B working together to do the same job, which is x hours).   In this case, the time needed for machine B to do the job must also be 2 hours:   1/2+1/2= 
<gadget id="calculator">  1/2+1/2</gadget>
<output>1</output>
1.   Now, plug x=1 and r=2 in the options to see which one yields 2. Only option E fits.   Answer: xr/(r-x).
<result>E</result>
Working simultaneously at their respective constant rates, Machines A and B produce 800 nails in x hours. Working alone at its constant rate, Machine A produces 800 nails in r hours. In terms of x and r, how many hours does it take Machine B, working alone at its constant rate, to produce 800 nails?