Question

A water tank has a capacity of 40,000 gallons. At 9 AM on October 1,
the tank was holding exactly 28,000 gallons. Water is being added to
the tank at a rate of 3 gallons per minute until it is filled. At the same
time, a hole in the tank is causing water to leak out at a rate of 1.8
gallons per hour.
QUESTIONS IN THE COMMENT

Answer 1

1.How much water is in the tank at noon on October 2?

2.When will the tank be filled?

3.If there had been no leak in the tank, when would it have been filled?

Answer 2

@mathmale Can you explain it?

Answer 3

This question has several different aspects to consider before we can do much work.
First of all, what is the shape of the tank? Is it cylindrical, conical, box-shaped or what? Is it possible that the shape of the tank doesn't matter?

Answer 4

It doesn't state

Answer 5

First consider the part of the problem that assumes the tank has a leak. We need to calculate the "net rate at which water is entering the tank." More water enters the tank than leaves it. What do you think is the "net rate?"

Answer 6

x= minutes 3x?

Answer 7

This is the water input rate: "Water is being added to
the tank at a rate of 3 gallons per minute"

What is the water outflow rate? It's given.

Answer 8

1.8(60x)

Answer 9

The inflow rate is 3 gallons per minute; the outflow rate is "a hole in the tank is causing water to leak out at a rate of 1.8
gallons per hour. " You could convert "3 gallons per minute" to "x gallons per hour, or you could convert 1.8 gallons per hour to "y gallons per minute."

Doesn't matter which. You choose one of these 2 and then make the conversion.

Answer 10

In: 180 gallons per hour and Out: 1.8 gallons per hour ??

Answer 11

Input is 180 gallons per hour. Right. You could leave the outflow as it is now: 1.8 gallons per hour.

So, what is the NET rate at which water enters the tank? Just subtract. show your work.

Answer 12

\[180-1.8= 178.2 \] 178.2 gallons per hour

Answer 13

Correct. Now, multiply that rate by 3 hours. Explain why "3 hours."

Answer 14

Why by 3? Isn't it 27 hours?

Answer 15

Yes. You realized that before I did. Very good!
Mult. 178.2 gallons per hour by your 27 hours.

Answer 16

4881.4 gallons

Answer 17

4811.4 ***

Answer 18

Is that the answer to Part 1 of this question? Why or why not?

Answer 19

Yes, because that would be the amount of water in the tank at noon on October 2 after calculating the rate.

Answer 20

I mean nooo

Answer 21

Still have to add 28000 gallons

Answer 22

Yes. The answer to my question is NO, because 4,811.4 is the additional water to the 28,000 gallons that were already in the tank at 9 am. Oct. 1st.

So, how many gallons are in the tank at noon on the 2nd?

Answer 23

32,811.4 gallons

Answer 24

Great. Now let's return to Square One. Starting with conditions as they were as of 9 a.m. Oct. 1st, how much water would filling the tank completely require?

Answer 25

12,000 gallons

Answer 26

Right. And the net inflow rate is 178.2 gal/min.
How long would it take to fill the tank completely, and on which day and at what time would that be done?

Answer 27

hour* ?

Answer 28

I got it now, thanks for the help

Answer 29

my pleasure. You're one of my Best Students.

Answer 30

Haha

Answer 31

Take care, Best Student. See you later.