At 9 o'clock......hands are separated by 1/4 * 360 = 90°
And, at this time.....let the minute hand be at 0°
And let the hour hand be at 270°
In 49 minutes.....the hour hand moves 360/12 * 49/60 = 24.5°
So.....the hour hand is at [270 + 24.5] = 294.5°
And the minute hand has moved [ 0 + 49/ 60 * 360 ] = 294°
So....they are separated by 0.5° = (1/2) of a degree
To find the exact time when they are together....
The hour hand moves at 30/60 = .5 degrees per miniute = (1/2)° per minute
The minute hand moves at (360/60) = 6° per minute
So....we need to solve this
294.5 + (1/2)M = 294 +(6)M where M is the number of minutes sfter 9:49
Subtract 294 and (1/2)M from both sides
.5 = 5.5M divide both sides by 5.5
.5 / 5.5 = M = 5/55 = 1/11
So....they will be together 1/11 of a minute ater 9:49 ≈ 5.45 seconds after 9:49
