The correct answer is "kept" but I don't understand why because shouldn't "over forty years" make it past progressive? This is from an ACT practice test. The passage talks about a guy making the clock on 1753 so maybe it is because the clock is not functional today?
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If all of the precise time-keeping (start to finish) was in the past, regardless of whether for 40 days or 40 years, then kept conveys the proper tense.
If the comment is about it keeping precise time from some point in the past continuing until the present time, then has kept would be correct.
I will expand on my earlier comment:
The question appears to require some extrapolation and inference that if the clock was built in 1753 and its accuracy was measured for the text to be accurate for 40 years then we have only accounted to the year 1793. 1753 to 2014 would be 261 years that are not tracked and we can presume the clock has not remained accurate well over the stated years.
In plain English:
The clock kept precise time for over forty years? (That it was accurate)
The clock has kept precise time for over 261 years. (Or until last checked or measured) because of the earlier inferences.