Algebra Solutions
Topics || Problems
In clock problems you usually calculate time and angles.
Clock Hands
- Minute Hand (Base)
- Hour Hand
- Seconds Hand
| Minute Hand | Second Hand | Minute Hand | Hour Hand |
|---|---|---|---|
| 1 min | 60 min | 1 min | 1/12 min |
| 2 min | 120 min | 2 min | 1/6 min |
| 30 min | 1800 min | 30 min | 5/2 min |
| ... | ... | ... | ... |
| n min | 60n min | n min | n/12 min |
This simply means that, if the minute hand moves n minutes the second hand moves 60n minutes and the hour hand moves n/12 minutes.
| Minutes | Angle (degree) from 12 |
|---|---|
| 15 | 90 |
| 30 | 180 |
| 60 | 360 |
Use this as a conversion unit, so if you like to calculate how many degrees is 12 minutes. 12 x 90 / 15 = 72 degrees
Solution:
sum forward (blue line) = \( 15 + 30/12 + \theta \)
sum backwards (black line) = 30
\(15 +30/12 +\theta \) = 30
\( \theta\) = 25 minutes = 75 degrees
Using the hour hand, rewrite it as described by minute hand. From 12 to 3 that's 15 minutes, from 3 to where it is now is 30/12 minutes(refer to the table above) and the rest up to 6 is unknown.
The minute hand just moves 30 minutes.
Another Solution:
Convert all minutes to degrees
15 minutes = 90 degrees
30/12 minutes = 15 degrees
30 minutes = 180 degrees
sum forward (blue line) = \( 90 + 15 + \theta \)
sum backwards (black line) = 180
\( 90 + 15 + \theta \) = 180
\( \theta\) = 75 degrees