Step-by-step explanation:
I've seen this before... I'm assuming your questions are the following:
A) How many gallons are there in the tub after 5 minutes?
To answer this, you need to know how many additional gallons of water there will be after 5 minutes. So if for every minute, a 1/2 gallon is added, then after 5 minutes, there will be how many gallons added?
Then, add the amount of gallons that were initially in the tub in order to get the total amount of water after 5 minutes.
You should get 8 1/2 gallons.
B) Write an equation using y as gallons and x as minutes.
For this problem, it is useful to utilize the equation of a line:
y=mx + b
Where m is the rate of change (slope), and b is where the water level is at when time begins "begins" (y-intercept).
We know the water level increases by 1/2 gallon every minute. So that is our m value. We also know that the tube starts at 6 gallons, so that is our b value. Therefore, we get:
Y = (1/2)x +6
C) Using part b, find how many minutes have passed for there to be exactly 23 3/4 gallons.
For this, we use our equation and solve for the number of minutes (x). This means we want to isolate x out get it all by itself. First, we subtract 6 from both sides:
y-6 = (1/2)x
Then, we need to get rid of the 1/2. So we multiply both sides by 2:
2(y-6) = x
Now, we plug in 23 3/4 for y and solve.
2(23 3/4 - 6) = x
2(17 3/4) = x
35 1/2 = x
So after 35 1/2 minutes, there will be 23 3/4 gallons in the tub.
Does that helpI've seen this before... I'm assuming your questions are the following:
A) How many gallons are there in the tub after 5 minutes?
To answer this, you need to know how many additional gallons of water there will be after 5 minutes. So if for every minute, a 1/2 gallon is added, then after 5 minutes, there will be how many gallons added?
Then, add the amount of gallons that were initially in the tub in order to get the total amount of water after 5 minutes.
You should get 8 1/2 gallons.
B) Write an equation using y as gallons and x as minutes.
For this problem, it is useful to utilize the equation of a line:
y=mx + b
Where m is the rate of change (slope), and b is where the water level is at when time begins "begins" (y-intercept).
We know the water level increases by 1/2 gallon every minute. So that is our m value. We also know that the tube starts at 6 gallons, so that is our b value. Therefore, we get:
Y = (1/2)x +6
C) Using part b, find how many minutes have passed for there to be exactly 23 3/4 gallons.
For this, we use our equation and solve for the number of minutes (x). This means we want to isolate x out get it all by itself. First, we subtract 6 from both sides:
y-6 = (1/2)x
Then, we need to get rid of the 1/2. So we multiply both sides by 2:
2(y-6) = x
Now, we plug in 23 3/4 for y and solve.
2(23 3/4 - 6) = x
2(17 3/4) = x
35 1/2 = x
So after 35 1/2 minutes, there will be 23 3/4 gallons in the tub.
Does that help
