Clock
Written on 11:32 pm by Vja Students
A clock is observed. The hour hand is exactly at the minute mark, and the minute hand is six minutes ahead of it. Later, the clock is observed again. This time, the hour hand is exactly on a different minute mark, and the minute hand is seven minutes ahead of it. How much time elapsed between the first and second observations?
Ans:The hour hand is exactly on a minute mark five times per hour -- on the hour, twelve minutes past the hour, twenty four minutes past, thirty six minutes past, and forty eight minutes past.
Let X be the number of hours, and Y be the number of minutes past the hour. When the hour hand is on a minute mark, the position of the hour hand is 5X + Y/12, and the position of the minute hand is Y. On the first occasion, Y = 5X + Y/12 + 6. This is equivalent to 60X = 11Y - 72. Since Y can only take one of the values in the set { 0, 12, 24, 36, 48 }, it can be determined that the only legal values for the equation are X = 1 and Y = 12. So the time is 1:12.
Similarly, the second occasion's equation is 60X = 11Y - 84. The only legal values here are X = 3 and Y = 24. So the time is 3:24.
Between 1:12 and 3:24, two hours and twelve minutes have elapsed.
clearly the clock as at 1:12 initially
and later at 3:24
so time is 2 hours and 12 mins
rahul the time interval u said is right. but it need not be the time u have mentioned.(from 1.12 to 3.24)
the clock can be initially at any position. that doesnt matter. after 2 hours and 12 mins the minute hand will be 7 mins ahead of hour hand. thats all..
65z+1 minutes...
z can be 1,2,3.....12
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Hannah was sitting in front of a clock. When she observed it for the first time, the hour hand was at a minute mark and the minute hand was six minutes ahead. After some time, she observed the clock again to find that the hour hand was exactly on a different minute mark and the minute hand was seven minutes ahead of its time. Can you calculate how much time has elapsed between two observations?