At what time between 6 and 7 o'clock will the hands of the clock be at right angles for the second time?
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6:05:27
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6:49:05
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6:21:49
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6:54:32
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None of these
At 6 o'clock, the hands are 30 minutes apart. For the second right angle, the minute hand must gain 45 minutes on the hour hand. Using the formula M = (2/11) * (30 * H +/- angle), for the second time, we use 6:00 + 45 minutes. M = (2/11) * (180 + 90) = 540/11 = 49 and 1/11 minutes. This corresponds to 6:49:05.
Using the formula for right angles, where the time in minutes is 5 times the hour plus or minus 15 multiplied by 12 divided by 11, we calculate the second instance after 6 o'clock. For the second time, we use the positive term, so the calculation is 5 times 6 plus 15, which equals 45. Multiplying 45 by 12 divided by 11 gives 540 divided by 11, which is 49 minutes and 5 seconds. Therefore, the hands will be at right angles for the second time at 6:49:05.