Trace: • answer
Answer
He is losing $2.60
To start, you need to know how wrong the clock is. Begin by calculating how long it takes an accurate clock's hands to cross.
Hour hand: 360o / (12hr * 3600sec/hr) = 1/120 o/sec
Minute hand: 360o / (1hr * 3600sec/hr) = 1/10 o/sec
relative speed between the two: 1/10 - 1/120 = 11/120 o/sec
time per overlap: 360 o / relative speed = 360 o / 11/120 * 3600sec/hr = 12/11 Hours
If the broken clock makes 1 overlap per 69 minutes, and the good clock makes 1 overlap per 12/11 hours, we can get a 'time dilation factor' of 69/(12/11*60)
This leaves us with a simple equation to find how much money he is losing or gaingng: $6 * 8hrs * 69/(12/11*60) - $6 * 8hrs = $2.60. Since the broken clock moves slower than it should, he is working more than 8 hours, so he is losing $2.60.