Tim has a working analog 12-hour clock with two hands that run continuously (instead of, say, jumping
on the minute). He also has a clock that runs really slow—at half the correct rate, to be exact. At
noon one day, both clocks happen to show the exact time. At any given instant, the hands on each
clock form an angle between 0 and 180 inclusive. At how many times during that day are the angles
on the two clocks equal
found it here http://goodmathsproblems.blogspot.com/

Question

amistre64 · Answer

in other words, how many times a day to they both show the same time?

anonymous · Answer

yeah

amistre64 · Answer

in one hour we have 1:00 versus 12:30 soo

12:00 12:00
01:00 12:30
02:00 01:00
03:00 01:30
04:00 02:00
05:00 02:30
06:00 03:00
07:00 03:30
08:00 04:00
09:00 04:30
10:00 05:00
11:00 05:30
12:00 06:00

01:00 06:30
02:00 07:00
03:00 07:30
04:00 08:00
05:00 08:30
06:00 09:00
07:00 09:30
08:00 10:00
09:00 10:30
10:00 11:00
11:00 11:30
12:00 12:00

once from what I can tell

amistre64 · Answer

but thats asking for equal angles; not equal times

amistre64 · Answer

we could set up a cosine wave and compare it to a cosine that has a period of twice as long

amistre64 · Answer

perhaps this will help http://www.wolframalpha.com/input/?i=y+%3D+cos%28x%29+and+y%3Dcos%28x%2F2%29+from+0+to+4pi