A certain toilet tank can be emptied in 6 sec through its drain when it is flushed. This happens at the same time that the water is flowing in through the inlet pipe. Withthe drain closed, the inlet pipe canfill the tank in 30 sec. How long would it take to drain the tank if the water was not flowingin through the inlet pipe?

Question

A certain toilet tank can be emptied in 6 sec through its drain when it is flushed. This happens at the same time that the water is flowing in through the inlet pipe. Withthe drain closed, the inlet pipe canfill the tank in 30 sec. How long would it take to drain the tank if the water was not flowingin through the inlet pipe?

Answer 1

in flow rate Q1 = 1 tank / 30 seconds

out flow rate = Q2

Q2 - Q1 = 1 tank/6 seconds

Q2 - 1/30 = 1/6
Q2 = 5/30 + 1/30 = 6/30 = 1/5 = 1 tank/5 seconds
so
5 seconds

Answer 2

let the tank hold 1 unit of volume

let the rate of water flowing in be y units/sec
let the water flowing out be x units / sec

When drain is open (water going in and out at the same time)
6(x-y) = 1
x - y = 1/6

drain closed: 30y = 1
y = 1/30

plug back into x-y = 1/6
x - (1/30) = 1/6
x = 1/5

only drain open:
t(1/5) = 1
t = 5 sec

With the drain only,
it would take 5 seconds to empty the tank

Answer 3

To solve this problem, let's break it down into two parts:

1. How long does it take to fill the tank with both the drain and inlet pipe open?

Given that the drain can empty the tank in 6 seconds and the inlet pipe can fill the tank in 30 seconds, we can calculate their combined filling and draining rate.

Let's denote the filling rate of the inlet pipe as F (in tanks per second) and the draining rate of the drain as D (in tanks per second).

Since the filling rate is the reciprocal of the filling time (30 seconds), we have:

F = 1/30 tanks per second.

Similarly, the draining rate is the reciprocal of the draining time (6 seconds), so:

D = 1/6 tanks per second.

To find the combined rate, we subtract the draining rate from the filling rate:

Combined rate (C) = F - D.

So, C = 1/30 - 1/6 = 1/30 - 5/30 = -4/30 = -2/15 tanks per second.

The negative sign indicates that the tank is being drained.

Now, if the drain and the inlet pipe are both open, the net filling rate becomes negative (-2/15 tanks per second). Therefore, the tank will be drained instead of filled, and we can say that the tank will never be completely filled.

2. How long does it take to drain the tank with only the drain open?

Now, let's consider the scenario where only the drain is open, and the inlet pipe is closed.

We know that the drain can empty the tank in 6 seconds. Therefore, if there is no water flowing in through the inlet pipe, it would take 6 seconds to completely drain the tank.

In summary, if the water is not flowing in through the inlet pipe, it would take 6 seconds to drain the tank.