Q3) If a tank is emptied in 5 minutes by a pump that is pumping at a rate of 300 gallons per minute, how long will it take to empty the tank with a pump that will pump at a rate of 500 gallons per minute?
since volume = rate*time,
300*5 = 500x
x = 3 minutes
or, 5/3 the speed, so 3/5 the time
To solve this problem, we need to use the concept of rates. We are given that a tank is being emptied in 5 minutes by a pump that is pumping at a rate of 300 gallons per minute.
Let's start by understanding the rate at which the tank is being emptied. The rate is given as 300 gallons per minute, which means that the pump can empty 300 gallons of water in one minute.
Now, let's find the total amount of water in the tank. Since the tank is being emptied in 5 minutes, the total amount of water in the tank is 300 gallons per minute multiplied by 5 minutes, which equals 1500 gallons.
Next, we need to find the time it will take to empty the tank with a pump that will pump at a rate of 500 gallons per minute. We can use the same logic as before.
Since the total amount of water in the tank is 1500 gallons, and the new pump has a rate of 500 gallons per minute, we can divide the total amount of water by the rate of the pump to find the time it will take to empty the tank.
1500 gallons ÷ 500 gallons per minute = 3 minutes
Therefore, it will take 3 minutes to empty the tank with a pump that pumps at a rate of 500 gallons per minute.
To summarize:
1. Calculate the total amount of water in the tank: 300 gallons per minute * 5 minutes = 1500 gallons.
2. Divide the total amount of water by the rate of the new pump: 1500 gallons ÷ 500 gallons per minute = 3 minutes.
So, it will take 3 minutes to empty the tank with a pump that pumps at a rate of 500 gallons per minute.