# Clock Problem

• Mar 3rd 2009, 04:51 PM
needhelp_21
Clock Problem
The minute hand and hour hand form a right angle at 3:00. How long after till they form a right angle again? Give the answer to the nearest second.
• Mar 3rd 2009, 05:23 PM
skeeter
Quote:

Originally Posted by needhelp_21
The minute hand and hour hand form a right angle at 3:00. How long after till they form a right angle again? Give the answer to the nearest second.

let the 12 position be $\theta = 0$

$t$ = time in seconds after 3 o'clock

position of the minute hand ...

$\theta_m = \frac{1}{10} \frac{deg}{sec} \cdot t$

hour hand ...

$\theta_h = 90 + \frac{1}{120} \frac{deg}{sec} \cdot t$

the next time they are 90 degrees apart, the minute hand will have passes the hour hand ...

$90 = \frac{1}{10} \cdot t - \left(90 + \frac{1}{120} \cdot t \right)$

solve for t in seconds
• Mar 3rd 2009, 06:03 PM
needhelp_21
I'm confused. How do I solve for t in seconds from that equation?
• Mar 4th 2009, 09:12 AM
skeeter
Quote:

Originally Posted by needhelp_21
I'm confused. How do I solve for t in seconds from that equation?

algebra?