# Thread: Volume of two tanks

1. ## Volume of two tanks

Having problems with this volume question.

There were 68000cm3 of water in tank X and tank Y. The heights of the water in both tanks are equal. Tank Y was 40% full of water. When all the water from tank Y was poured into tank X, 4litres of water overflowed.

A) find the height of the water in tank X at first?
B) find the capacity of tank Y?

2. Hello, spaarky!

A challenging problem . . . I haven't solved it yet.

$\displaystyle \text{There are 68 liters of water in tank }X\text{ and tank }Y.$
$\displaystyle \text{The heights of the water in both tanks are equal.}$
$\displaystyle \text{Tank }Y\text{ is 40\% full of water.}$
$\displaystyle \text{When the water from tank }Y\text{ is poured into tank }X,$
. . $\displaystyle \text{4 liters overflowed.}$

$\displaystyle \text{(A) Find the height of the water in tank }X\text{ at first.}$
$\displaystyle \text{(B) Find the capacity of tank }Y.$

This how I envision the two tanks and the water.

Code:
        Tank X         Tank Y

*       *
|       |
|       |     *           *
|       |     |           |
* - - - *     * - - - - - *
|:::::::|     |:::::::::::|
h|:::A:::|    h|:::::B:::::|
|:::::::|     |:::::::::::|
*-------*     *-----------*

There are $\displaystyle A$ liters of water in tank $\displaystyle X.$

There are $\displaystyle B$ liters of water in tank $\displaystyle Y.$

We know that: .$\displaystyle A + B \:=\:68$

We see that: .$\displaystyle A+B \,=\,68$ is 4 more than the capacity of tank $\displaystyle X.$

. . Hence, the capacity of tank $\displaystyle X$ is 64 liters.

We know that $\displaystyle \,B$ is 40% of the capacity of tank $\displaystyle Y.$

I need at least one more equation . . . Where is it?

3. Exactly .... It's like on the tip of my tongue ... but no matter what I have written down so far doesn't quite get there.

Base Area (BA)
We also know the Ratio of BAa : BAb is the same as the Ratio of the Volume A : B.

Also, for Capacity
X : Y
64 : B / .4
160 : B
So Y --> 160/B x X
Y --> 10240/B

And I think there is a mistake in here somewhere

Also,
The Base Area doesn't change so with a common Height,
64 : 2.5B is also the the same as BAa : BAb --> A : B

A : B --> 64 : 2.5B

4. i view this as two rectangular tanks with the same base areas.Tank y has a capacity of 170 liters and tank x 132liters.Tank y is simply taller

bjh

5. I don't believe this is feasible.

If the capacity of X : Y is 132 : 170

Then, the original volume of water in Y would be 170 x 40% = 68

This is the full amount of combined water. Thus the Height of the water in both Tanks, originally, would not be the same as indicated in the question.