Question

the inlet pipe on a water tank can fill the tank in 8 hrs. when the tank was full, both the inlet pipe and the drainpipe were accidentally opened. twenty four hours later, the tank was empty. how many hours would it take to empty a full tank if only the drain were open

Answer 1

I believe we must assume that the take empties/fills at constant rates.

Answer 2

Let \(f\) be the fill time and \(d\) be t he drain time.

Answer 3

well, I mean fill rate and drain rate

Answer 4

We know that the size of the tank is \(8f\) and it is \(24(f-d)\).
So you are trying to find \(t\) such that \(td\) is the side of the tank.

Answer 5

You want to find \(t\). You have two equations: \[
24(f-d)=8f\\
td = 8f
\]

Answer 6

@KawasumiKimiko Do you know how to solve this?

Answer 7

quadratic?

Answer 8

No, you can use substitution

Answer 9

Okay, can you isolate \(d\) in the first equation?

Answer 10

distribute 24?

Answer 11

Yeah, try that first

Answer 12

24f-24d=8f

Answer 13

Okay, you are close, but can you isolate \(d\)?

Answer 14

uhm. subtract 24f from both sides & then divide both sides by -24?

Answer 15

yes

Answer 16

so d=16f/-24

Answer 17

Yes

Answer 18

Now plug that in for \(d\) in the second equation

Answer 19

You'll be able to solve for \(t\), because the \(d\) cancels.

Answer 20

Can you do it?

Answer 21

I might have another approach to the problem, if the answer is right :p

Tank filled in an hour = 1/8
Tank emptied in an hour = 1/B... assuming B is total drain time
Total time for the tank to completely fill or drain when both the pipes are left open = 24 hrs

1/8 + 1/B = 1/24
1/B = 32/192
B = 6 hrs..