using a certain garden hose, liza can fill her fancy new bucket with water in 45 seconds. Unfortunately, Henry accidently makes a hole in the bucket, so if initially full, the bucket will now become empty in 1 minute. How long will it take to fill the bucket, considering it has a hole in it?

counting in seconds,

1/45 - 1/60 = 1/x
x = 180

so, it will take 3 minutes

To find out how long it will take to fill the bucket considering it has a hole in it, we need to determine the rate at which water is leaking from the bucket.

Let's assume that the rate at which water is leaking is L liters per minute.

Given that Liza can fill the bucket with water completely in 45 seconds, we can assume that the flow rate of the hose is such that it fills the bucket with B liters of water in 45 seconds.

Converting the filling rate from seconds to minutes:
B liters / 45 seconds * (60 seconds / 1 minute) = B * (60/45) liters per minute = (4/3) * B liters per minute.

Since we now know the filling rate is (4/3) * B liters per minute, and we assume the leaking rate is L liters per minute, we can write the equation:

Filling rate - Leaking rate = Net filling rate

(4/3) * B - L = Net filling rate

The net filling rate is determined by how much water is filling the bucket after accounting for the leaking rate. In this case, if the initial bucket is full, it will become empty in 1 minute due to the leak. Therefore, the net filling rate is equal to the leaking rate:

(4/3) * B - L = L

To find the value of L, we solve for B:

(4/3) * B = 2L

B = (3/2) * L

Substituting B in the net filling rate equation:

(4/3) * (3/2) * L - L = L

2L - L = L

L = L

From the equation, we see that L = L, which means the leaking rate is equal to itself. This implies that no matter how fast water is being supplied, the bucket will empty at the same rate, making it impossible to fill the bucket with a hole in it.

Therefore, the bucket cannot be filled with water when it has a hole in it.