In a week, how many times are the hands of clock at right angles with each other?
If you switch to a rotating coordinate system in which the hour hand stands still, then the minute hand makes only 11 revolutions, and so it is at right angles with the hour hand 22 times. In a 24 hour day you get $$2\times 22= 44$$
so in weekthere are 7 days
$$7\times 44= 308 times$$
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