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
if the supply pump can pump p gal/min,
and the outlet pumps each draw q gal/min,
30(p-q) = 8450
45(p-2q) = 10950
(p,q) = (320,115/3)
Now you can convert that to gal/hr.
Let's assume the pumping rate of the supply pump is S gallons per hour, and the pumping rate of each outlet pump is O gallons per hour.
We are given the following information:
1. With one outlet pump running, the supply pump can increase the fuel level in the storage tank by 8450 gallons in 30 minutes.
- This means that in 30 minutes, the supply pump pumps 8450 gallons of fuel, which is equivalent to (8450/30) = 281.67 gallons per minute.
- Converting this to gallons per hour: (281.67 * 60) = 16900 gallons per hour.
2. With both outlet pumps running, the supply pump can increase the fuel level in the storage tank by 10,950 gallons in 45 minutes.
- This means that in 45 minutes, the supply pump pumps 10,950 gallons of fuel, which is equivalent to (10950/45) = 243.33 gallons per minute.
- Converting this to gallons per hour: (243.33 * 60) = 14600 gallons per hour.
Since both outlet pumps are assumed to have identical pumping rates, we can divide the overall increase in fuel level with both pumps running (14600 gallons per hour) by 2 to find the pumping rate of each outlet pump.
Therefore, the pumping rate of each outlet pump is: 14600 / 2 = 7300 gallons per hour.
So, the pumping rate for the supply pump is 16900 gallons per hour, and the pumping rate for each outlet pump is 7300 gallons per hour.
To find the pumping rate in gallons per hour for each of the pumps, we need to determine how many gallons each pump can pump in one hour.
Let's start by finding the pumping rate of the supply pump. We are given that the supply pump can increase the fuel level in the storage tank by 8,450 gallons in 30 minutes. To find the pumping rate in gallons per hour, we need to convert the time to hours.
1 hour = 60 minutes
Therefore, the supply pump can increase the fuel level by 8,450 gallons in (30/60) = 0.5 hours.
So, the pumping rate for the supply pump is:
Pumping rate for supply pump = 8,450 gallons / 0.5 hours = 16,900 gallons/hour.
Next, let's find the pumping rate for each outlet pump. We are given that with both outlet pumps running, the supply pump can increase the fuel level in the storage tank by 10,950 gallons in 45 minutes.
To find the pumping rate in gallons per hour, we need to convert the time to hours. Again, 1 hour = 60 minutes.
So, with both outlet pumps running, the supply pump can increase the fuel level by 10,950 gallons in (45/60) = 0.75 hours.
To find the pumping rate for each outlet pump, we divide the total increase in fuel level (10,950 gallons) by the time in hours (0.75 hours) and divide it equally between the two outlet pumps since they are identical.
Pumping rate for each outlet pump = (10,950 gallons / 0.75 hours) / 2 = 14,600 gallons/hour.
Therefore, the pumping rate for the supply pump is 16,900 gallons/hour and the pumping rate for each outlet pump is 14,600 gallons/hour.