The volume of water inside a swimming pool doubles every hour. If the pool is filled to its
full capacity within 8hours, in how many hours was it filled to one quarter of its capacity?
Help step
It'll be half full in 4 hours.
When will it be 1/4 full? Remember that it doubles every hour.
To solve this problem, let's analyze the information given. We know that the volume of water inside the swimming pool doubles every hour and that it is filled to its full capacity within 8 hours.
If we denote the initial volume of the swimming pool as "V," after 1 hour it would be 2V (doubled), after 2 hours it would be 4V (doubled again), and so on.
Now, we need to determine how many hours it took for the pool to be filled to one-quarter of its capacity.
To do this, let's consider the fraction of capacity filled at each hour. After 1 hour, the pool is filled to 1/2 of its capacity (2V/4V = 1/2). After 2 hours, it is filled to 1/4 (4V/4V = 1), and after 3 hours, it is filled to 1/8 (8V/4V = 1/8).
From this analysis, we can see a pattern emerging. The fraction of capacity filled after n hours is given by 1/2^n.
Since we want to determine the number of hours it took to fill one-quarter of the capacity, we need to solve the equation 1/2^n = 1/4.
To simplify the equation, we can rewrite 1/4 as 2^-2 (since 2^-2 = 1/4).
Now, we have the equation 1/2^n = 2^-2.
To solve this equation, we can set the exponents equal to each other:
n = -2
Therefore, it took the pool -2 hours to be filled to one-quarter of its capacity.
However, this doesn't make physical sense since time cannot be negative. This means that the pool was never filled to one-quarter of its capacity, given the doubling rate of the volume of water every hour.