At what time between 6 and 7 pm will the minute hand be 90 degrees ahead of your hand?

Question

At what time between 6 and 7 pm will the minute hand be 90 degrees ahead of your hand?

Answer 1

If we carefully note we would find that  the angular speed of –

Hour-hand =  0.5 degree / min  and that of  Min-hand = 6 degree / min.

Let us consider the moment when it is 6.00 O’clock. The Min-hand is behind the Hour-hand by 180 degree.  Let us now assume that the Min-hand reaches the required position after 12 O’clock mark in            Ã¢Â€Â˜ x ‘ min, sweeping an angle  =  6 x  degree.  In order to keep the lead by 90 degree the Min-hand has to sweep through an angle  =  ( 180 + 90 + 0.5 x ) degree with an angular speed = 6 degree per min.

Hence  ( 180 + 90 + 0.5 x ) / x   =   6

=>   x  =  2700/55  =  49.091 min.

Hence  the Min-hand will lead the Hour-hand by 90 degree at   6  hr : 49.091 min ……………. Answer

Dr. P.K.Tandon

Answer 2

The above answers, 6:15 and 6:30 are wrong.

I assume you are trying to figure out when the minute hand will be 90 degrees ahead of the HOUR hand, not "your hand".

This is obviously your homework. Go ahead and copy some answer from here, you will get it wrong, not show any working, and get 0 marks.



Or, you could actually think about the mathematics of the question.

6:15 is wrong because by that time, the hour hand has moved a bit past the "6", and the angle will be a bit more than 90 degrees.

Write down an equation that shows the position of the hour hand as starting from the "6" and moving at a certain speed, as a function of time. Write down another equation that shows the position of the minute hand at the "12" (you can think of that as position "0") and moving at a different speed, as a function of time. Now figure out how to calculate the angle between the hands, as a function of time. Then, figure out the value of time such that the angle is 90 degrees (which, on the clock, is 3 "numbers" apart) - your answer is that time after 6pm.

Answer 3

6:15