Each day at noon a mechanical wristwatch was compared with
WWV time signals. The watch was not reset. It consistently
ran late, as follows: June 24, late 4 s; June 25, late 20 s; June 26,
late 34 s; June 27, late 51 s.
(a) For each of the three 24-hour intervals, calculate the rate
at which the wristwatch lost time. Express your answer in
seconds lost per hour.
(b) What is the average of the rates of loss found in part (a)?
(c) When the wristwatch shows 10h30m on June 30, what is
the correct WWV time? Do this calculation with the
average rate of loss of part (b) and also with the largest
rates of loss found in part (a). Estimate to within how
many seconds the wristwatch can be trusted on June 30
after the correction for rate of loss has been made.