Explanation

The rates in this question can be expressed in terms of the units . The rate of the two machines working together is the sum of the independent rates. Therefore, we can write



The first term is Machine A's rate, the second is Machine B's rate, and the rate on the right side is their combined rate. We can get rid of the fractions by multiplying both sides of the equation by abc:











This doesn't appear in the answer choices, so we can reformat by multiplying by 1:



For an alternate method, we can test with values. For example, looking at our first equation above, if a=20 and b=10, then both machines produce one widget together. Combined, they should produce twice as fast, so c=10. Plugging a and c into our solution, we can see whether we get b: That worked as planned. Indeed, these values for c and a do not yield a proper value for b in any of the other equations. The correct answer is (D).