A clock is started at 15 00.The clock is not working correctly and is slow.The clock loses 8 minutes every hour so after one hour the clock shows 15 52.What time will the clock show 3 21 hours after it is started?................................................. [2](e) The times on two clocks are checked regularly.One clock is checked every 6 days.The other clock is checked every 8 days.Both clocks are checked on 1st January 2021.Find the number of days during 2021 when both clocks will be checked on the same day.[There are 365 days in 2021.]................................................. [4]
Question
A clock is started at 15 00.The clock is not working correctly and is slow.The clock loses 8 minutes every hour so after one hour the clock shows 15 52.What time will the clock show 3 21 hours after it is started?................................................. 2 The times on two clocks are checked regularly.One clock is checked every 6 days.The other clock is checked every 8 days.Both clocks are checked on 1st January 2021.Find the number of days during 2021 when both clocks will be checked on the same day.[There are 365 days in 2021.]................................................. [4]
Solution
Let's break down the questions:
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The clock loses 8 minutes every hour. After 3 hours and 21 minutes (or 3.35 hours), the clock would have lost 3.35 * 8 = 26.8 minutes. However, since a clock can't show fractions of a minute, we'll round this up to 27 minutes. So, if the clock was started at 15:00, after 3 hours and 21 minutes, the time should be 18:21. But because the clock is slow and has lost 27 minutes, the clock will show 17:54 (18:21 - 27 minutes).
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For the second question, we need to find the least common multiple (LCM) of 6 and 8 to determine how often both clocks are checked on the same day. The LCM of 6 and 8 is 24. So, every 24 days, both clocks are checked on the same day. There are 365 days in 2021, so 365 divided by 24 equals 15.21. Since we can't have a fraction of a day, we round down to 15. Therefore, during 2021, both clocks will be checked on the same day 15 times.
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