奧林匹克數學問題

after conctrcting the diagram, you will find x-y is actually the sum of the angles between two hour ends and the two minute ends

for hour ends, it completes 1 rotation in 12 hours, i.e. 720 minutes
therefore for each minute, it passes through 0.5 degree.

consider the angle between vertical line and the hour end at 2:34,
it is 2*60 + 34 = 154 minutes from 12:00, therefore the angle is 77degrees

consider the angle between vertical line and the hour end at 4:32,
it is 4*60 + 32 = 272 minutes from 12:00, therefore the angle is 136degrees

therefore difference = 59degrees

for the minute ends, it completes 1 rotation in 60 minutes, therefore in 1 minute, it passes through 6degrees
the difference bwtween the two minute ends = 2 min
therefore the angle between them = 2*6 = 12degrees

so x-y = 59 + 12 = 71degrees

71!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

在2時34分，時鐘上時針和分針所成的鈍角是x度，在4時32分，時鐘上
時針和分針所成的銳角是y度，求x－y
Sol
分針每分鐘走360度/60=6度
時針每分鐘走30度/60=0.5度
12點時兩針重合
12點到2時34分共154分
分針共走6*154=924度
時針共走0.5*154=77度
924度－77度=847度
x=847－2*360=127

12點時兩針重合
12點到4時32分共272分
分針共走6*272=1632度
時針共走0.5*272=136度
1632度－136度=1496度
y=1496－4*360=56
x－y=127－56=71

x=((60-34)/60)*30+30*3+4*6=127
y=((60-32)/60)*30+30+2*6=56
so,
x-y=127-56=71