Question

A large fish tank already has 12 gallons of water in it. A hose continues to fill it at a rate of 1/3 of a gallon per minute. Another fish tank already contains 3 gallons of water and is filled at the rate of 1 1/2 times the rate of the first hose.
Both hoses are turned on at the same time. Determine the number of minutes until both fish tanks contain the same number of gallons of water.

Answer 1

First things first, let's convert 1/2 and 1/3 to the LCD (Least Common Denominator)

Answer 2

What would the LCD be?

Answer 3

The LCD of what...?

Answer 4

1/2 and 1/3

Answer 5

6

Answer 6

the LCD is 6, correct.

so that means we have
3/6 and 2/6

this will make it easier to calculate how much faster it fills.

for every 3/6ths of a gallon, the other tank is filled 1 and 2/6ths times more, what is 1 and 2/6ths times 3/6?

Answer 7

2/3

Answer 8

I got this backwards....

1 and 3/6ths * 2/6ths

sorry about that x.x

Answer 9

I'm not sure, to be honest ;\

Answer 10

1/2

Answer 11

Which means we have gone full circle... :|...









It's been a while since i've done this and I'm very rusty

Answer 12

I don't know where to go from here >_<... lemme get someone who might know

Answer 13

Ah, okay. Well, thanks ^^

Answer 14

Let x = gallons per minute
Let y = number of minutes until both tanks have the same amount of gallons
12 + (1/3)x = y
3 + (1 + 1/2)(1/3)x = y

Set y = y, then solve for x

Answer 15

^I take it that that's a continuation to what Ultrilliam said?

Answer 16

So to sum it up here's a sentence description of what was supposed to be done:

Gallons Currently in Tank 1 PLUS Rate of 1st hose TIMES x = y
Gallons Currently in Tank 2 PLUS Rate of 2nd hose TIMES rate of 1st hose TIMES x = y

Answer 17

Hope that's not too confusing for you.

Answer 18

I think I get it...thanks.

Answer 19

Great...You're welcome.

Answer 20

Let us know what you get for the answer.

Answer 21

Actually
x = minutes until both tanks have same amount of gallons and
y = total gallons of water in both tanks (which should be the same amount).

Answer 22

I notice there's still three people currently looking at this question. Has anyone come up with an answer or is everyone still in a state of confusion?

Answer 23

Yeah..I'm still confused..

Answer 24

I'm sorry, that's my fault. You may have been confused by my initial descriptions for x and y. The truth is, I "rushed" those descriptions because I was pre-occupied with something else I was doing before I saw this question and I was trying to type the solution quickly and get back to what I was doing before. If I went over the steps of how to solve the problem here, do you think that would help you understand better?

Answer 25

Yes, please.

Answer 26

Okay, here's the full solution for this problem:

First, we should let
x = minutes until both tanks have same amount of gallons and
y = total gallons of water in either tank (which should be the same amount).

Next, we should write out the following verbal expression as follows:

Gallons Currently in Tank 1 PLUS Rate of 1st hose TIMES x = y
Gallons Currently in Tank 2 PLUS Rate of 2nd hose TIMES rate of 1st hose TIMES x = y

Afterwards, we input the numbers into the verbal expression:
12 + (1/3)x = y
3 + (1 + 1/2)(1/3)x = y

Next set the two expressions equal to each other since y = y
12 + (1/3)x = 3 + (1 + 1/2)(1/3)x

Finally, Solve for x:
12 + x/3 = 3 + (1 + 1/2)(x/3)
12 + x/3 = 3 + x/3 + x/6
12 = 3 + x/6
9 = x/6
54 = x

So it will take 54 minutes for the tanks to be filled with the same amount of gallons.

By the way, if you're curious, 30 gallons is the amount that will be in both tanks after 54 minutes.

Answer 27

If anyone still has more questions after this, I can provide a clearer detailed description of the solution steps.