Final answer:
The time it takes for the furnace to perform one revolution using 1/2 cubic foot of gas at 142.8 cubic feet per hour is 0.210 minutes, or approximately 12.6 seconds.
Step-by-step explanation:
The student is asking to determine the time it takes for a furnace to perform one revolution, given its gas consumption rate. To find this, we need to calculate the time taken for the furnace to use 1/2 cubic foot of gas at the rate of 142.8 cubic feet per hour (ft³/hr).
We start by converting the hourly rate to a per minute rate since we are dealing with a small volume (1/2 ft³) which will likely take less than an hour to consume:
Divide 142.8 ft³/hr by 60 minutes to get the consumption rate per minute.
Calculate the time taken to use 1/2 ft³ by dividing by the per minute rate.
Converting to minutes: 142.8 ft³/hr ÷ 60 minutes/hr = 2.38 ft³/minute. Now, to find the time (t) for 1/2 ft³, we use t = Volume/Rate:
t = 0.5 ft³ ÷ 2.38 ft³/minute = 0.210 minutes, or approximately 12.6 seconds per revolution.