Pool Filling & Emptying: Calculating Capacity & Rate

[chawki]

Homework Statement

The total capacity of the pool is 1000 cubic meters. the filling of the pool started on Thursday morning at 6 o’clock. On Friday morning at 9 o’clock when the pool was being filled, the pump for removal of water was started by mistake. Starting from this point onwards, water was both added and removed from the pool.
The pool became empty on Monday evening at 6 o’clock pm (18:00). It can be assumed that the rate at which the water was added and removed were both constant.

Homework Equations

a) When would the pool have been full if the pump to remove the water had not been
started? State in your answer the day of the week and the time of the day with the
accuracy of one hour. You can solve the problem graphically or mathematically.
b) How many cubic meters of water does the removing pump get rid of in 24 hours?

The Attempt at a Solution

How should we use the rate here?
we know that it was filling for 108 hours and emptying for 81 hours, But then?

 

[eumyang]

Seems like a piece of info is missing from the problem. There is no indication of the amount of water in the pool at a certain point in time. If we had this piece of info, we can certainly find the rates at which the water was added and removed. Are you sure this is the entire problem?

 

[chawki]

Yes, i copied it as it was given!

 

[Mentallic]

I second what eumyang said.

It tells us the capacity of the pool, but not at the rate it can be filled or emptied, or at what level the water was when the emptying started. Not enough info...

 

[HallsofIvy]

Assuming that the pool started empty, let the rate at which the first pump fills the pool be $r_1$ cubic feet per hour and the rate at which the second pump empties the pool be $r_2$ feet per hour. From 6:00 Thursday morning to 9:00 Friday morning is 27 hours so there would be $27r_1$ cubic feet of water in the pool at that time. After that, with both pumps running, the water is coming in at [itexs]r_1- r_2[/itex] cubic feet per minute Since that cause the pool to eventually become empty again, $r_1$ must be less than $r_2$ so that $r_1- r_2$ is negative. In fact, it takes 81 hours to empty the pool so we must have $27r_1+ 81(r_1- r_2)= 108r_1- 81r_2= 0$ so that $81r_2= 108r_1$ so that $r_2= (4/3)r_1$.

But that single equation is not enough to determine $r_1$ and $r_2$ separately, which is what would be need to answer the questions.

 

[Mentallic]

Assuming that the pool started empty, let the rate at which the first pump fills the pool be $r_1$ cubic feet per hour and the rate at which the second pump empties the pool be $r_2$ feet per hour. From 6:00 Thursday morning to 9:00 Friday morning is 27 hours so there would be $27r_1$ cubic feet of water in the pool at that time. After that, with both pumps running, the water is coming in at [itexs]r_1- r_2[/itex] cubic feet per minute Since that cause the pool to eventually become empty again, $r_1$ must be less than $r_2$ so that $r_1- r_2$ is negative. In fact, it takes 81 hours to empty the pool so we must have $27r_1+ 81(r_1- r_2)= 108r_1- 81r_2= 0$ so that $81r_2= 108r_1$ so that $r_2= (4/3)r_1$.

But that single equation is not enough to determine $r_1$ and $r_2$ separately, which is what would be need to answer the questions.

Oh, now we can finish answering the questions!

a) When would the pool have been full if the pump to remove the water had not been
started? State in your answer the day of the week and the time of the day with the
accuracy of one hour.