A fuel storage tank has one supply pump and two identical outlet pumps. With one outlet pump running, the supply pump can increase the fuel level in the storage tank by 8450 gallons in 30 minutes. With both outlet pumps running, the supply pump can increase the fuel level in the storage tank by 10,950 gallons in 45 minutes. Find the pumping rate, in gallons per hour, for each of the pumps.
supply pump _____ gal/h
each outlet pump _____ gal/h
To find the pumping rate for each of the pumps, we can use the formulas:
Pumping rate = Amount of fuel pumped / Time
Let's first find the pumping rate for the supply pump.
Supply pump's pumping rate:
In 30 minutes, one outlet pump can empty the tank by 8450 gallons.
Therefore, the pumping rate for one outlet pump = 8450 gallons / 30 minutes.
To find the pumping rate per hour, we need to convert 30 minutes to hours:
30 minutes = 30/60 hours
= 0.5 hours
Pumping rate for one outlet pump = 8450 gallons / 0.5 hours
Now, let's find the pumping rate for both outlet pumps running.
In 45 minutes, both outlet pumps can empty the tank by 10,950 gallons.
Therefore, the pumping rate for both outlet pumps = 10,950 gallons / 45 minutes.
To find the pumping rate per hour, we need to convert 45 minutes to hours:
45 minutes = 45/60 hours
= 0.75 hours
Pumping rate for both outlet pumps = 10,950 gallons / 0.75 hours
Therefore, the pumping rates are as follows:
Supply pump: (8450 gallons / 0.5 hours) = 16,900 gallons per hour
Each outlet pump: (10,950 gallons / 0.75 hours) = 14,600 gallons per hour
To find the pumping rate in gallons per hour for each of the pumps, we can use the formula:
Pumping rate = Volume / Time
First, let's find the pumping rate of the supply pump.
With one outlet pump running, the supply pump can increase the fuel level in the storage tank by 8450 gallons in 30 minutes.
Therefore, the pumping rate of the supply pump with one outlet pump running is:
Pumping rate = 8450 gallons / 30 minutes
To convert the time to hours, we can divide it by 60:
Pumping rate = 8450 gallons / (30 minutes / 60 minutes per hour)
Simplifying:
Pumping rate = 8450 gallons / (0.5 hours)
Pumping rate = 16,900 gallons/hour
So, the pumping rate of the supply pump is 16,900 gallons/hour.
Now, let's find the pumping rate of each outlet pump.
With both outlet pumps running, the supply pump can increase the fuel level in the storage tank by 10,950 gallons in 45 minutes.
Therefore, the pumping rate of the supply pump with both outlet pumps running is:
Pumping rate = 10,950 gallons / 45 minutes
Converting the time to hours:
Pumping rate = 10,950 gallons / (45 minutes / 60 minutes per hour)
Simplifying:
Pumping rate = 10,950 gallons / (0.75 hours)
Pumping rate = 14,600 gallons/hour
Since there are two identical outlet pumps, we can divide this pumping rate by 2 to find the individual pumping rate for each outlet pump:
Pumping rate of each outlet pump = 14,600 gallons/hour / 2
Pumping rate of each outlet pump = 7,300 gallons/hour
Thus, the pumping rate of the supply pump is 16,900 gallons/hour, and the pumping rate of each outlet pump is 7,300 gallons/hour.