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An empty pool has the capacity to hold $2700 \text{ cubic feet } (\text{ft}^3)$ of water. A particular hose fills this pool with water at a rate of $25\text{ft}^3$ per minute. If the hose is placed into the empty pool and turned on, approximately what percent of the pool will be filled with water after $1$ hour?

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Exponential growth and decay: word problems

Full solution

Q. An empty pool has the capacity to hold

2700 \text{ cubic feet } (\text{ft}^3)

of water. A particular hose fills this pool with water at a rate of

25\text{ft}^3

per minute. If the hose is placed into the empty pool and turned on, approximately what percent of the pool will be filled with water after

1

hour?

Identify values: Identify the values given in the problem. $\newline$ The pool's capacity is $2700 \, \text{ft}^3$ . $\newline$ The rate at which the hose fills the pool is $25 \, \text{ft}^3$ per minute. $\newline$ We need to find out how much of the pool is filled after $1$ hour.
Convert time: Convert the time from hours to minutes. $\newline$ Since the rate of the hose is given in minutes, we need to convert the time from hours to minutes. $\newline$ $1$ hour = $60$ minutes
Calculate volume: Calculate the volume of water filled by the hose in $1$ hour. Multiply the rate at which the hose fills the pool by the number of minutes in $1$ hour. Volume filled in $1$ hour = $25 \, \text{ft}^3/\text{minute} \times 60 \, \text{minutes}$ Volume filled in $1$ hour = $1500 \, \text{ft}^3$
Calculate percentage: Calculate the percentage of the pool that will be filled. $\newline$ Divide the volume filled in $1$ hour by the total capacity of the pool and multiply by $100$ to get the percentage. $\newline$ Percentage filled = $\frac{\text{Volume filled in 1 hour}}{\text{Pool's capacity}} \times 100$ $\newline$ Percentage filled = $\frac{1500 \text{ ft}^3}{2700 \text{ ft}^3} \times 100$
Perform division: Perform the division and multiplication to find the percentage. $\newline$ Percentage filled = $(1500 / 2700) \times 100$ $\newline$ Percentage filled = $0.5556 \times 100$ $\newline$ Percentage filled = $55.56\%$

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