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 q hours. In terms of x and q, how many hours does it take Machine B, working alone at its constant rate, to produce 800 nails?  Choices:  A) x/(x+y)  B) y/(x+y)  C) xy/(x+y)  D) xy/(x-y)  E) xq/(q-x)
Pick some smart numbers for x and q.   Say x=1 hour and q=2 hours (notice that q must be greater than x, since the time for machine A to do the job, which is q 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 q=2 in the options to see which one yields 2. Only option E fits.   Answer: xq/(q-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 q hours. In terms of x and q, how many hours does it take Machine B, working alone at its constant rate, to produce 800 nails?