math/physics
posted by Samuel on .
Estimate the percentage savings in the fuel bill if the thermostat is set back from 68 degrees F to 50 degrees F for 12 hours of the day, and left at 68 degrees F for the other 12 hours, assuming an outside temperature of 15 degrees F all day.

The amount of heat per unit time that leaks out of the house is approximately proportionate to difference between the inside and outside temperature. The thermostat will make sure that as much heat is produced by the heating as is leaking away, so that thee temperature stays constant on average.
So, if the thermostat is left at 68 F all day, the total amount of heat used per day will be some constant c times (6815), while if it is set at 50 F for half a day and 68 for the other half, you'll use
1/2 c (5015) + 1/2 c (6815)
per day.
c (68  15) = 53 c
1/2 c (5015) + 1/2 c (6815) =
44 c
44c/(53 c) = 0.83
So, you save 17%