I have an old alarm clock, on which the hands move at only 95% of the speed that they should do. I need it to wake me up at 7.30 am, so every night, at 10.30pm, I change the time shown on the

clock so that it will show the correct time at 7.30 am when the alarm goes off.

(a) What time does the clock show at 10.30 pm, immediately before I change it?

(b) What time do I change it to?

Please help immediately!!!

9514 1404 393

  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.

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.