Question

I have an old alarm clock, on which the hands move at only 95% of the speed that they should do.

Answer 1

9514 1404 393

Answer:

  a) 9:45 pm

  b) 10:57 pm

Step-by-step explanation:

In the 15 hours between 7:30 am and 10:30 pm, the clock hands will have moved 15×0.95 = 14.25 hours = 14 hours and 15 minutes.

At 10:30 pm, the clock indicates 9:45 pm.

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b) In the 9 hours between 10:30 pm and 7:30 am, the clock will have moved 9×0.95 = 8.55 hours, or 8 hours 33 minutes. That is, the clock needs to be set 27 minutes ahead of the actual time.

The clock need to be set to 10:57 pm.

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Alternate solution

At 95% speed, the clock loses 5%×60 minutes = 3 minutes each hour. In the 15 hours from morning to night, the clock will be 45 minutes slow. It will indicate 9:45 at 10:30 pm.

In the 9 hours from night to morning, the clock will lose 27 minutes so needs to be set 27 minutes fast. It should be set to 10:57 pm at 10:30 pm.