SOLUTION: It is now between 9am and 10 o'clock am. In 4 minutes, the hour hand of a clock will be directly opposite the position occupied by the minute hand 3 minutes ago. What time is it?
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Question 1091616: It is now between 9am and 10 o'clock am. In 4 minutes, the hour hand of a clock will be directly opposite the position occupied by the minute hand 3 minutes ago. What time is it? Answer by ikleyn(52824) (Show Source):
Let the current time under the question be 9 hours and "t" minutes, where t is the real number, so t can be fraction of minutes and seconds.
The minute hand is at angular position of radians, counting from it vertical position at 9:00 am.
*** Minute hand makes its full revolution of radians in 60 minutes. ***
The hour hand at this moment is at the angular position radians, counting from its vertical position at midnight.
*** Hour hand has the angular velocity 12 times less than the minute hand: it is 12 times slower. ***
Three minutes ago the minute hand was in position of radians.
In four minutes the hour hand will be in position of radians.
Therefore, the governing equation is
= .
The major part is done: the equation/the model is set up.
The rest is just arithmetic.
As the first step, cancel in both sides and multiply by 60 both sides. You will get
t - 3 = ====>
= ====> = = = {{55/3}}} ====>
t = . = 20 minutes
