Answer
see solution
Work Step by Step
Assume one is more efficient than the other. Run the less efficient one in reverse (as a refrigerator) using the fraction of the work from the more efficient engine that the less efficient engine would produce running forward. At that point, there is zero net heat flow from the hot reservoir and the differential in work between the two engines is comes from the net heat removed from the cold heat reservoir. This contradicts the Carnot assumption.
