A mathematically inclined friend emails you the following instructions: "Meet me in the cafeteria the first time after 2:00 p.m. today that the hands of a clock point in the same direction." When should you meet your friend?
* 2: 21:41
(hr : min : sec)
the hour is given , but my answers are wrong
clearly 2:21:41 is wrong. Draw the clock hands for that time.
The minute hand moves at 6°/min
The hour hand moves at 30°/hr = 0.5°/min
So, to find when the hour and minute hands point in the same direction, m minutes must have passed, so that
60+0.5m = 6m
5.5m = 60
m = 10.90909 = 10 10/11 minutes
Now express in hr:min:sec
To determine the time at which the hands of a clock point in the same direction, we need to find a time where the minute hand and the hour hand align.
Let's break down the problem:
1. The minute hand completes a full rotation every 60 minutes.
2. The hour hand completes a full rotation every 12 hours, which is equivalent to 720 minutes.
To find the time at which the hands align, we need to compare the respective positions of the hands.
At 2:00 p.m., the minute hand is pointing at the 12, and the hour hand is pointing at the 2.
We now need to calculate the minute hand's rotation since 2:00 p.m.:
The minute hand makes 21 revolutions (21 x 360 degrees) and an additional 41 minutes, which corresponds to another rotation of (41/60 x 360 degrees). Adding these two values gives us the total rotation of the minute hand from 2:00 p.m.
For the hour hand, we need to calculate its angular rotation since 2:00 p.m:
The hour hand moves at a rate of (1/12 x 360 degrees) per hour. Taking into account that it has been 21 hours since 2:00 p.m., the total rotation of the hour hand can be calculated.
Next, we need to determine the relative rotation between the minute and hour hands:
To find the difference in rotation between the minute and hour hands, we subtract the rotation of the hour hand from the rotation of the minute hand.
Finally, we divide the relative rotation by the difference in rotation rate between the minute and hour hands to find the time at which they align.
However, to solve this problem using this method, we need the exact time, including seconds. The given time of "2:21:41" is not enough to provide a definitive answer.