Question

Jada walks up to a tank of water that can hold up to 10 gallons.When it is active, a drain empties water from the tank at a constant rate. When Jade first see the tank it contains 7 gallons of water. Three minutes later, the tank contains 5 gallons of water.
A. At what rate is the amount of water in the tank changing?

B. How many more minutes will it take for the tank to drain completely.

C. How many minutes before Jada arrived was the water tank completely full

Answer 1

Answer:

Part A)The amount of water in the tank is changing at -2/3 gallons per minute.

Part B) it will take 7.5 minutes for the tank to drain completely.

Part C) The water tank was completely full 4.5 minutes before Jada arrived.

Step-by-step explanation:

Information fetching:

• 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

Part A) At what rate is the amount of water in the tank changing?

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 -2/3 gallons per minute. Hence, the amount of water in the tank is changing at -2/3 gallons per minute.

Note: negative sign indicates the number of gallons of water are decreasing.

Part B) How many more minutes will it take for the tank to drain completely.

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

So, it will take 7.5 minutes for the tank to drain completely.

Part C) How many minutes before Jada arrived was the water tank completely full

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

So, the water tank was completely full 4.5 minutes before Jada arrived.

Keywords: time rate of change, time

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