Title 11 Clock Problem.pdf ✅

MSTC 11: Clock Problems For an analog clock, The minute hand moves around the circle with 60-minute marks in one hour. Meanwhile, the hour hand moves just from one hour mark to another, with 5-minute marks. Thus, the hour hand moves 12 times slower than the minute hand. Angles between the hands are more conveniently expressed in terms of minute marks than angle measures. Conversion from angle measure to minute marks can be done using ratio and proportion with 60-minute marks in 360°. For example, What time after 5 AM will the hands of the clock be at a right angle for the first time? From an analog clock showing 5 AM, In the initial position, the hour hand is ahead (in the clockwise direction) by 25-minute marks to the minute hand. When the minute hand moves by x minutes, the hour hand moves by x/12. Thus, their final positions are minute hand = x hour hand = 25 + x 12 For the distance in the final position knowing that the hands are at a right (90°) angle, distance 90° = 60 360° distance = 15 Initial position Final condition