What is the angle, in degrees, between the two hands of an analog Clock at 9:49? And at what EXACT time will the two hands be on top of each other? Thank you for help.

Guest Nov 16, 2018

edited by
Guest
Nov 16, 2018

#1**+2 **

The hour hand moves 360 degrees/(12 hours x 60 min) degrees each minute= 0.5 degrees/min

9 hours 49 min = 589 minutes or 294.5 degrees

The minute hand moves 360degrees/60 min = 6 degrees / min

49 minutes x 6 degrees/min = 294 degrees

294.5 - 294 = .5 degrees between the hands at 9 49

ElectricPavlov
Nov 16, 2018

edited by
Guest
Nov 16, 2018

#2**+2 **

The hands will be atop each other at what time?

270 + .5 x = 6x x = 270/5.5 = 49.0909090909090909

or 9:49 .090909*60 = 9:49:05.45454

ElectricPavlov
Nov 16, 2018

edited by
Guest
Nov 16, 2018

edited by Guest Nov 16, 2018

edited by Guest Nov 16, 2018

#3**+2 **

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

CPhill
Nov 16, 2018