Length of the minute hand on a watch is mm.

Length of the hour hand on a watch is mm.

Assume the angle between the minute hand and hour hand as .

Let the distance between the tips of the hands as .

Apply cosine rule to the  triangle in the figure.

Differentiate on each side with respect to . 

At one o clock angle between the hands is

Find :

Minute hand gives radians for one hour.

Hour hand gives radians for hours.

Therefore, for one hour hour hand gives .

Change in the angle with respect to time is

rad/hr.

Find the distance between the tips of the hands when the time is one o clock. 

Consider the expression (1) .

Substitute in the above expression.

 Find the distance between the tips of the hands is changing at one o clock.

Consider the expression (2) .

Substitute , and in above expression.

Distance between the tips of the hands is changing at one o clock is mm/hr.

Distance between the tips of the hands is changing at one o clock is mm/hr.