Question

Score:

IS
2) Erick walks up to a tank of water that can hold up to 16 gallons. When it is active, a drain
emptles water from the tank at a constant rate. When Erick first sees the tank, it contains 10
gallers of water. Four minutes later, the tank contains 7 gallons of water.
A) At whatrate is the amount of water in the tank changing? Use a signed number, and
include the unit of measurement in your answer.
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B) How many more minutes will it take for the tank to drain completely? Explatz or show
er min
your reasoning
C) How many minutes before Erick arrived was the water tank completely full? Explain or
show your reasoning.

Answer 1

-3/4 gallons per minute, 13 and 1/3 minutes, 8 minutes.

Explanation:

A) It says that when Erick first sees the tank, there is 10 gallons. But then, 4 minutes later, there is 7. That would show that it decreased 3 gallons in 4 minutes, and we find the unit rate by dividing both numbers by 4 to get 3/4 gallons in 1 minute. Because it's decreasing, it's -3/4 gallons per minute.

B) Since it starts at 10, and decreases constantly at 3/4 gallons per minute, dividing 10 by 3/4 would result in the time it takes. (We can also use an equation that starts with 10, and decreases 3/4 every x minutes, resulting in 0. This is the equation: 10-(3/4)x=0. Then we could add (3/4)x to each side, and divide each side by (3/4) to solve for x. This is just another way. You don't have to use it this way if it's a little complicated.) So, 10/(3/4)= 10*(4/3)=13 and 1/3 minutes for the bathtub to drain completely.

C) The tank is full at 16 gallons, and currently it's 10 gallons. We know the rate of change is 3/4 gallons per minute. If it starts at 16 gallons, the original, after we subtract 3/4 multiplied by x minutes (the rate), we get 10 gallons as the current amount. The equation would be 16-(3/4)x=10. Then we just add (3/4)x to each side and subtract 10 from each side to get 6=(3/4)x, and dividing each side by 3/4 would result in x minutes as 8 minutes to drain the tank. Hope this helps!