PSA_PRACTICE_QNR30. A clock is broken. But its hour hand, minute hand, and second hand still move at constant speeds in the normal direction. The second hand passes the hour hand every 10 seconds (measured by an accurate clock) and passes the minute hand every 20 seconds. How often does the minute hand pass the hour hand?
Let the speed of second, minute and hour hands be ‘s’, ‘m’ and ‘h’.
The second hand passes the hour hand every 10 seconds:
Consider the second and hour hand are together at some moment.
Total distance to be covered =360 degrees.
Relative speed= (s-h).
360/(s-h) =10 => s-h=36 ……(A)
Similarly, the second hand passes the minute hand every 20 seconds:
Relative speed= (s-h)
360/(s-m) =20 => s-m=18 ……(B)
Subtracting (B) from (A),
Thus, minute hand will pass the hour hand after:
=360/18= 20 seconds.