Answer:
<em>Part A)</em><em>The amount of water in the tank is changing at </em><em>-2/3 gallons per minute. </em>
<em>Part B) </em><em>it will take </em><em>7.5 minutes</em><em> for the tank to drain completely.</em>
<em>Part C) </em><em>The water tank was completely full </em><em>4.5 minutes</em><em> before Jada arrived.</em>
Step-by-step explanation:
<em>Information fetching:</em>
- Tank of water can hold up-to 10 gallons.
- When it is active, a drain empties water from the tank at a constant rate.
- 7 gallons of water present in the tank when Jade first saw
- 5 gallons of water left after 3 minutes
<em>Part A) At what rate is the amount of water in the tank changing?</em>
As the gallons were decreased from 7 to 5 in three minutes. It means in three minutes, 2 gallons were decreased.
So, gallons per minute change would be <em>-2/3 gallons per minute. </em>Hence, <em>the amount of water in the tank is changing at </em><em>-2/3 gallons per minute. </em>
<u><em>Note</em></u><u><em>: </em></u><u>negative sign indicates the number of gallons of water are decreasing.</u>
<em>Part B) How many more minutes will it take for the tank to drain completely.</em>
Let 'm' be the number of minutes will it take for the tank to drain completely.
As,
(2/3 gallons per minute) (m minutes) = 5 gallons
So,
m = 5 (3/2)
= 15/2
= 7.5 minutes
<em>So, it will take </em><em>7.5 minutes</em><em> for the tank to drain completely.</em>
<em>Part C) How many minutes before Jada arrived was the water tank completely full</em>
As tank of water can hold up to 10 gallons. So, the tank of water is full when there is 10 gallons of water. So, this is 3 gallons of water more than the total 7 number of gallons at the time when Jada arrived.
As Jada arrived when the tank had left 7 gallons.
Let 'm' be the number of minutes before Jada arrived when the water tank was completely full.
So,
(2/3) (m) = 3
m = 3(3/2) = 9/2
= 4.5 minutes
<em>So, the water tank was completely full </em><em>4.5 minutes</em><em> before Jada arrived.</em>
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<em>Keywords: time rate of change, time</em>
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Learn more about time rate of change from brainly.com/question/6279456</em>
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