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