Can anyone answer this Math problem? pls help?

Question

It takes a pipe 12 hours to fill a tank when the faucet at the base of the tank is open. If the faucet is opened 2 hours after the pipe had started running, 3/4 of the tank is filled after an hour. How long will it take the faucet to empty a half-filled tank if the pipe is not running?

use variables x and y, like 1/x - 1/y =1/12

Answer 1

The pipe fills the tank at an unknown rate of p, which has units tanks/hr. The faucet empties the tank at an unknown rate of f, which also has units tanks/hr. We are told that with the pipe and faucet both running, it takes 12 hours to fill the tank, so we know that p - f = (1/12) tank/hr. We also know that if the pipe runs for two hours and then the faucet is opened, the tank will be 3/4 full after an additional hour. Therefore, (2 hr)(p) + (1 hr)(p - f) = (3/4) tanks. Let's rewrite these equations.

p - f = 1/12
2p + (p - f) = 3/4 ==> 3p - f = 3/4

Now we can rewrite each of them again, isolating f.

f = p - 1/12
f = 3p - 3/4

Now set them equal to each other.

p - 1/12 = 3p - 3/4
8/12 = 2p
p = 1/3

Now we can use the value of p to find f.

f = p - 1/12 = 1/3 - 1/12 = 1/4

So if the faucet drains at a rate of (1/4) tank/hr, it would take 2 hours for the faucet to drain half a tank.

Answer 2

I believe that this problem reversed the meanings of pipe and faucet but I'll solve it as written.

Let T be the volume of the tank, P be the flow rate of the pipe and F be the flowrate of the faucet.

If the pipe is filling the tank and the faucet is emptying the tank then if both are open and the tank is filling up, the pipe's flow rate must be greater than the faucet's. 12 hours of this net flow rate fills the tank.

(1) 12P - 12F = T

If the pipe is open for 2 hours and then the faucet is opened for one hour after that, the tank is ¾ filled.

(2) 2P + (P-F) = ¾T
(3) 3P - F = ¾T

Multiply (3) by 4

(4) 12P - 4F = 3T

Subtract (1) from (4)

(5) 8F = 2T
(6) 2F = ½T

This means it would take 2 hours for the faucet to empty half the tank.

Answer 3

Let
p = filling rate of the pipe in volume/sec, like cu ft/hr
f = discharge rate of faucet at the bottom of the tank

with faucet open, the filling rate is p - f
and it fills the tank in 12 hours, so
volume of tank = V = 12 (p - f) cu.ft

with faucet closed, volume of tank filled after 2 hours = 2p
In the next hour, with faucet open, it fills additional p - f
so
2p + p - f = 3V/4 = (3/4) 12 (p - f)
3p - f = 9 (p - f) = 9p - 9f
6p = 8f
p = (4/3)f
and
V = 12(p - f) = 12 ( 4f/3 - f) = 12f/3 = 4f

so with the pipe not running, f = V/4, faucet can drain 1/4 of tank per hour, thus
A half-filled tank will take the facut TWO HOURS to empty
Ans: 2 hours

Answer 4

2/3 of the tank is filled in 2 hours by the pipe alone
therefore the whole tank is filled in 3 hours..
and the faucet can drain the entire tank in 4 hours..
now time it will take to drain the half filled tank is 1/2*4=2 hours..your answer is 2 hours

Answer 5

What subject of math is this question in? I don't know what technique I'm supposed to use.