Basically, you have 2^4 plates to test, and 4 machines. This obviously hints of binary. You create a series of combinations to each plate occurs in a unique combination of testers.
Based of the binary system, you make combinations so all different options are created. '0' means a plate is not included in the tester sample, '1' means it is included.
Such a way is shown below:
The test shows that there's 16 unique tester combinations, matching the 16 different outcomes for the 4 testers. Therefor, matching the results of the 4 testers in 55 minutes, means you have 20 minutes to prepare the samples and make the correct conclusion.
Rather then calculating (which you could fail in stressy situations) you can just look up which 'plate' matches the positive readings from the testers. If you insist on calculating, you could convert the readings to decimal, but you'd have to increase the result by 1 (plates start at 1, binary count at 0)
In the example above, you could see that if testers 1,2 and 4 come back negative, and tester 3 is positive, you know for certain plate 3 is the poisoned plate.