Lesson Gaining clock problem
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<H2>Gaining clock problem</H2> <H3>Problem 1</H3>A clock is set right at 10:00 am. The clock gains 10 min in 24 hours. What will the true time when it indicates 3:00 pm the following day? <B>Solution</B>. <pre> Let {{{T[g]}}} be the reading displayed by the gaining clock and {{{T}}} be the reading of a correct clock. Since {{{T[g]}}} gains 10 minutes every 24 hours = 60*24 minutes, we have {{{T[g]}}} = 1450 when {{{T}}} = 1440. So, the ratio {{{T[g]/T}}} = {{{1450/1440}}} = {{{145/144}}}, and the inverse ratio {{{T/T[g]}}} = {{{144/145}}}. The difference between <U>the readings of the gaining clock</U> at 10:00 am "today" and 3:00 pm "tomorrow" {{{DELTA}}}{{{T[g]}}} is 24 + 5 = 29 hour marks, or {{{29*60}}} minute marks. (Notice that I am talking about the difference measured in "minute marks", not in real minutes in this case !) It corresponds to {{{(29*60)*(144/145)}}} minutes of CORRECT TIME. Now calculate: {{{(29*60)*(144/145)}}} = 1728 minutes = 28 hours and 48 minutes. </pre> <U>Answer</U>. When the gaining clock indicates 3:00 pm of the following day, the correct clock shows exactly 2:48 pm. 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