Working simultaneously at their respective constant rates, Machines A

Since there is no restriction given that a and b must be different, let's assume that Machine A and Machine B have the same rates. => a=b.

Let's take some small numbers and see how that works out:

Let a = b = 2, which means both Machines A and B need 2 hours each independently to produce 20 widgets.
Combined, they'll need half the time, namely 1 hour to produce 20 widgets => c = 1

What happens if we plug-in these numbers now?
Before we do that we have to keep in mind that we are looking for the time that b needs to produce 10 widgets.
Therefore our target value = b/2 = 1.

First we see that we can immediately rule out answers A) and B) as we'd divide an even number ac or 2ac with an uneven number a+c. That would not result in an integer value.

(A)ac/a+c =>2/3, no
(B)2ac/a+c =>4/3, no
(C)ac/2a+2c => 2/6, no
(D)ac/2a-2c => 2/2, yes!
(E)ac/2c-2a => 2/-2, no

Answer (D)