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The Minute Hand Of A Clock Overtakes The Hour Hand At Intervals Of 64 Minutes Of Correct Time. How Much A Day Does The Clock Gain Or Lose? |
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Answer» Simple EXPLANATION by Juned: The minute hand overtakes hours hand 11 times in 12 hours Therefore the time taken by the minute to overtake = (12 * 60)/11 = 65.4545 minutes In this CLOCK the minute hand is taking 64 minutes to overtake Therefore in 12 hours it will overtake 720/64 = 11.25 times That means 0.25 times more in 12 hours or 0.5 times more in a day HENCE, the clock gains = 0.5 times of the normal time ⇒ 65.4545 * 0.5 = 32.72 minutes or 360/11 minutes Explanation by a4academics x be distance traveled by hour hand Then distance traveled by minute hand = 1 + x Time = Distance/Rate ⇒ x/(1/12) = (1 + x)/1 ⇒ x = (1/12)(1 + x) = 1/12 + x/12 ⇒ (11/12)x = 1/12 x = 1/11 Calculate time for minute hand to travel a distance 1 + x. Time = Distance/Rate (1 + x)/1 = 1 + x = 1 + 1/11 = 12/11 hour Actual time to overtake on clock is 64 minutes. 64 min = 64/60 hours = 16/15 hour Correct Clock Speed/Actual Clock Speed (12/11) / (16/15) = 12*15 / (11*16) = 180/176 = 45/44 The clock gains: 45/44 - 1 = 1/44 day = 24/44 hour = 6/11 hour = 360/11 min = 32 min and 434/11 sec. Simple explanation by Juned: The minute hand overtakes hours hand 11 times in 12 hours Therefore the time taken by the minute to overtake = (12 * 60)/11 = 65.4545 minutes In this clock the minute hand is taking 64 minutes to overtake Therefore in 12 hours it will overtake 720/64 = 11.25 times That means 0.25 times more in 12 hours or 0.5 times more in a day Hence, the clock gains = 0.5 times of the normal time ⇒ 65.4545 * 0.5 = 32.72 minutes or 360/11 minutes Explanation by a4academics Let x be distance traveled by hour hand Then distance traveled by minute hand = 1 + x Time = Distance/Rate ⇒ x/(1/12) = (1 + x)/1 ⇒ x = (1/12)(1 + x) = 1/12 + x/12 ⇒ (11/12)x = 1/12 x = 1/11 Calculate time for minute hand to travel a distance 1 + x. Time = Distance/Rate (1 + x)/1 = 1 + x = 1 + 1/11 = 12/11 hour Actual time to overtake on clock is 64 minutes. 64 min = 64/60 hours = 16/15 hour Correct Clock Speed/Actual Clock Speed (12/11) / (16/15) = 12*15 / (11*16) = 180/176 = 45/44 The clock gains: 45/44 - 1 = 1/44 day = 24/44 hour = 6/11 hour = 360/11 min = 32 min and 434/11 sec. |
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