Question

Five clocks are being tested in a laboratory. Exactly at noon, as determined by the WWV time signal, on successive days of a week the clocks read as in the following table. Rank the five clocks according to their relative value as good timekeepers, best to worst. Justify your choice

Short answer

The ranking of the clocks as a good timekeeper, best to worst is C, D, A, B, E.

Step-by-step solution

Understanding the time difference in the clock

None of the clocks move by exactly 24 hours in a 24-hour period, but this isn't the most significant requirement for evaluating their accuracy in measuring time intervals. Each 24-hour period, the clock advances by the same (or nearly the same) amount. The interval can then be readily altered by adjusting the clock reading.

The chart below shows the corrections (in seconds) that must be made to each clock's reading throughout a 24-hour period.

No clock described above advanced by exactly in a whole day period. The clock should also be consistent with the readings to make the corrections possible.

Finding the ranking of the clocks

The entries can be determined by subtracting the clock reading at the end of the interval from the clock reading at the beginning.

Clock	Sun - Mon	Mon-Tue	Tue-Wed	Wed-Thu	Thu-Fri	Fri-Sat
A	-16	-16	-15	-17	-15	-15
B	-3	+5	-10	+5	+6	-7
C	-58	-58	-58	-58	-58	-58
D	+67	+67	+67	+67	+67	+67
E	+70	+55	+2	+20	+10	+10

Clock C and D are consistent with clock readings. But the correction in C is lesser that the correction in D. So, clock C should be the best timekeeper followed by clock D. Corrections, which must be applied to clock A range from 5 s to 17 s and the range for clock B is -5 s to + 10 s ; for clock E, it is -70 s to -2s . So, after D, the best timekeepers would be clock A and clock B and the worst timekeeper would be clock E.

Thus, the final ranking of the clocks is C, D, A, B, E.