After 10 minutes, the container goes from 5 gallons to 3 gallons. So in those 10 minutes, the container loses 2 gallons (5-3 = 2)
Rate = (amount of water lost)/(amount of time elapsed) Rate = (-2)/(10) Rate = -1/5 Rate = -0.2
The rate is -0.2 gallons per minute. The negative indicates we have a loss of water. So every minute, the container loses 0.2 gallons (or 1/5 of a gallon). This is the slope. The slope measures rate of change.
Final Answer for part A is 0.2 gallons per minute In fraction form, the answer would be 1/5 of a gallon per minute
The slope found from part A was -0.2, so let m = -0.2 The container initially holds 5 gallons of water, so this is the y intercept. Call this b = 5
Together m = -0.2 and b = 5 will be plugged into y = mx+b to get y = -0.2x+5
The equation y = -0.2x+5 represents how much water is left x = time in minutes y = amount of gallons left over
To find out when the container is empty, plug in y = 0 and solve for x y = -0.2x+5 0 = -0.2x+5 0-5 = -0.2x+5-5 -5 = -0.2x -0.2x = -5 -0.2x/(-0.2) = -5/(-0.2) x = 25
It will take 25 minutes for the container to empty
A. The container starts with 5 gallons. After 10 minutes it has 3 gallons. That means that 2 gallons leaked out in 10 minutes. The rate water is leaking at is (2 gal)/(10 min) = 0.2 gallons per minute
b. (5 gal)/(0.2 gal/min) = 25 min
The container will be empty 25 minutes after it started leaking.
There are 5 people who can be guards, 2 will be guards. Since each person has the same chance of becoming a guard, each person has a 2/5 chance of being a guard which makes it unlikely for Diana to become a guard.
