The time is 9:00. On a 12-hour clock, how many minutes elapse before the hour hand and minute hand are 28 degrees apart for the first time?
+298 At 9:00, the hands form a right-angle (90°) or you can think of it as 270° if you look at the angle between the minute and the hour hand.
MINUTE HAND RATE:
Now the minute hand moves 1/60 of the way around the circle each minute. 1/60 of 360° is 6°
The minute hand moves 6° per minute.
HOUR HAND RATE:
The hour hand moves 1/12 of the way each hour. Dividing by 60, that means the hour hand moves 1/720 of the way around the circle each minute. 1/720 * 360° = ½°
The hour hand moves ½° per minute.
Thus the minute hand is getting 6° closer, but the hour hand is moving away at a rate of ½° per minute. That's a net of 5½° per minute that they are getting closer together.
You want to figure the minutes until the 270° angle is down to 28°.
Set up an equation:
270 - 5.5t = 28
270 - 28 = 5.5t
242 = 5.5t
t = 242/5.5
t = 484/11
t = 44
Answer:
In 44 minutes (at 9:44).
+298 At 9:00, the hands form a right-angle (90°) or you can think of it as 270° if you look at the angle between the minute and the hour hand.
MINUTE HAND RATE:
Now the minute hand moves 1/60 of the way around the circle each minute. 1/60 of 360° is 6°
The minute hand moves 6° per minute.
HOUR HAND RATE:
The hour hand moves 1/12 of the way each hour. Dividing by 60, that means the hour hand moves 1/720 of the way around the circle each minute. 1/720 * 360° = ½°
The hour hand moves ½° per minute.
Thus the minute hand is getting 6° closer, but the hour hand is moving away at a rate of ½° per minute. That's a net of 5½° per minute that they are getting closer together.
You want to figure the minutes until the 270° angle is down to 28°.
Set up an equation:
270 - 5.5t = 28
270 - 28 = 5.5t
242 = 5.5t
t = 242/5.5
t = 484/11
t = 44
Answer:
In 44 minutes (at 9:44).
