Please reason step by step, and put your final answer within \boxed{}.
Suppose the 28 machines have varying work rates, with each machine i completing Wi units of work per day (i = 1, 2, ..., 28). Given that all 28 machines can complete the work in 10 days, find the number of machines, M, required to complete the same work in 40 days. Assume that each machine has a unique work rate, and we can use any combination of machines existing among the 28 to complete the work.
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