Question

Starting at noon,how long will it take for the hour hand and the minute hand of a typical clock to form a 90 degree angle?

Answer 1

15 min

Answer 2

the answer is 180/11 hours

Answer 3

i think that answer is in mins, not hours. I got 3/11 of an hour for an answer, which is 180/11 mins.

Answer 4

180/11 hours is well over 12 hours, it shouldnt take more than 30 mins for the right angle to happen.

Answer 5

The interesting assumption you have to make is whether the hands move continuously or in ticks, as Joe assumes. The tick assumption does seem valid though, and his work looks right at first glance.

Answer 6

Doesn't matter if they move continuously or in ticks. the answer will be the same.

Answer 7

Simplest solution I can think of is to just express the position of each hand in terms of time.
t = time in hour
M = position of minute hand in degrees from starting position = 360*t
H = position of hour hand in degrees from starting position = (360/12)*t = 30t

Angle between the two is equal to the difference in positions, so 360t - 30t = 330t

Setting 330t = 90 and solving for t gives 90/330 hours or 16.36 minutes.

Which does match Joe's answer.

Answer 8

Computationally, dhatra, sure. Maybe you can get the same answer assuming ticks. Realistically though, is there such a tick representing 16.36 minutes? No. There would be a 16 minute tick and a 17 minute tick. Depending on the clock, obviously. Which is why I think it's an interesting assumption to consider.

Answer 9

Still, we get the same answer each way. 16.36 ticks represents 16.36 minutes after the hour.

Answer 10

Except you have to consider how often the hands actually move. If the minute hand ticks at the end of each minute and the hour hand ticks at the end of every 12 minutes, then the answer you get is much different.

After 12 minutes the hour hand ticks for the first time and doesn't tick again until 24 minutes.

So when the minute hand is on tick 16, the hour hand is on tick 1 and the hands are 15 ticks apart, which represents 90 degrees. So 16 minutes exactly is the first time they would be 90 degrees apart and not 16.36.