Question 1186342: At exactly 12 o’clock noon the hour hand of a clock begins to move at twice its
normal speed, and the minute hand begins to move backward at half its normal
speed. When the two hands next coincide, what will be the correct time?
Found 3 solutions by greenestamps, Edwin McCravy, ikleyn:
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
The normal angular speed for the hour hand is 30 degrees per hour, clockwise of course. So starting at 12:00 noon this clock's hour hand starts moving at 60 degrees per hour, still clockwise.
The normal angular speed for the minute hand is 360 degrees per hour, clockwise. So starting at 12:00 noon this clock's minute hand starts moving at 180 degrees per hour, counterclockwise.
For the hands to meet after 12:00, the two hands need to move a total of 360 degrees.
Let t be the number of hours after 12:00 where the hands meet again.
60t+180t=360
240t=360
t=360/240=3/2 or 1.5
ANSWER: It will take 1.5 hours starting at 12:00 for the two hands to meet again; so the correct time will be 1:30pm.
Answer by Edwin McCravy(20056)  (Show Source):
You can put this solution on YOUR website! At exactly 12 o’clock noon the hour hand of a clock begins to move at twice its
normal speed, and the minute hand begins to move backward at half its normal
speed. When the two hands next coincide, what will be the correct time?
A normal hour hand moves 360 degrees in 12 hours or 30 degrees per hour.
A normal minute hand moves 360 degrees per hour.
On this abnormal clock, beginning at noon, the hour hand moves clockwise at 60
degree per hour.
On this abnormal clock, beginning at noon, the minute hand moves counter-
clockwise at 180 degrees per hour.
At noon the hands are together and can be considered to be either 0 degrees or
360 degrees apart. At noon, the angle between the hands begins decreasing from
360 degrees at the rate of the sum of their speeds (because the hands are
approaching each other), which is 180+60=240 degrees per hour. The angle between
them will decrease from 360 degrees to 0 degrees in 360/240 = 1.5 hours, which
will be at 1:30 PM.
Edwin
Answer by ikleyn(52790)  (Show Source):
You can put this solution on YOUR website! .
At exactly 12 o'clock noon the hour hand of a clock begins to move at twice its normal speed,
and the minute hand begins to move backward at half its normal speed.
When the two hands next coincide, what will be the correct time?
~~~~~~~~~~~~~~~~~~~~
The normal angular speed of the hour hand is 360/12 = 30 degrees per hour;
so, its doubled speed is 60 degree per hour.
The normal angular speed of the minute hand is 360 degrees per hour;
so, half of its speed is 180 degrees per hour.
Thus, in this problem, the hour hand rotates anti-clockwise at 60 degrees per hour;
the minute hand rotates clockwise at 180 degrees per hour.
They approach each other at the rate of (60+180) = 240 degrees per hour.
So, they coincide next time in 360/240 = 1 = 1.5 hours = 90 minutes.
When the clock hands coincide next time, the correct time is 1:30 pm. ANSWER
Solved.
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