physics electricity question?

Question

an energy efficient air conditioner draws 7 amps in a standard 120 volt circuit. it cost $40 more than a standard air conditioner that draws 12 mps. if electricty cost 8 cents per kilowatt hour, how long would you have to run the efficient air conditioner to recoup the difference in price.

Answer 1

The standard unit consumes 120 X 12 / 1000 kwh per hour

The efficient unit consumes 120 X 8 / 1000 kwh per hour

Difference per hour is 120 X 5 /1000 kwh

Cost per hour in dollars is 120 X 5 X 8 / 100000

Capital Cost difference is 40 dollars

So if 'x' is the number of hours needed to recoup the capial cost through energy savings, we can write

x = (40 X 100 X 1000) / (120 X 5 X 8) = 1000 / 12 = 83.33 hours

The power factor is ignored here but in real life cannot be ignored.

Answer 2

Disregarding power factor (which in this case is not the best thing to do)
0.8*120*7t/1000 + 40 = 0.8*120*12t/1000
t = 40*1000/(0.8*120(12-7)
t = 83. hr 20 min.
Assuming a 60% power factor (which is not unreasonable for a small single-phase motor),
t = 138 hr. 53 min.