you have a barrel with water. after 30 seconds there is 14 gallons left. one minute you have 9 gallons left. determine the time the barrel was empty.
If after 30 seconds there are 14 gallons left, and after 60 seconds there are 9 gallons left,
Then you can see that in the 30 second gap, 5 gallons leaked out. So water is emptying at 5 gallons/30 seconds or 1 gallon every 6 seconds.
Can you use this rate of emptying and the initial number of gallons given to find the time?
i am getting 35 min and 7 sec. is that right?
No. How can you get more than a half hour for 9 gallons when 1 gallon is emptied every 6 seconds?
To determine the time when the barrel was empty, we can use the given information and apply a linear equation.
Let's first define the variables:
- Let "T" represent the time it took for the barrel to become empty, in seconds.
- Let "R" represent the rate at which the water is draining, in gallons per second.
We are given two data points:
1) After 30 seconds, there are 14 gallons left.
2) One minute (which is 60 seconds) later, there are 9 gallons left.
Using the first data point:
After 30 seconds, there are 14 gallons left. We can set up the equation:
14 = R * 30
Using the second data point:
One minute (60 seconds) later, there are 9 gallons left. We can set up the equation:
9 = R * 60
Now we have a system of two equations:
14 = R * 30
9 = R * 60
To solve the system of equations, we can divide the second equation by 2 to simplify it:
4.5 = R * 30
Now we have two equations:
14 = R * 30
4.5 = R * 30
We can solve these equations simultaneously to find the value of R:
14 = R * 30
4.5 = R * 30
Dividing the equations:
14/4.5 = (R * 30) / (R * 30)
3.111 ≈ 1
Now we have the value of R: R ≈ 1
Next, we can substitute the value of R back into one of the original equations to determine the time it took for the barrel to become empty.
Using the first equation:
14 = R * 30
14 = 1 * 30
14 = 30
This equation is inconsistent, which means there is no value of R that satisfies both equations. Therefore, there seems to be a mistake or inconsistency in the given information, as the data cannot be correct.
Without accurate information, we cannot determine the exact time when the barrel was empty.