A pool drains water at a rate of 3% every 5 minutes how many gallons of water are left after 50 minutes? How long will it take to have less then 1,000 gallons?
5 minutes depletes 3% of water
1 minute depletes 3/5 % of water
50 minutes depletes (3/5)(50) % or 30% of water
We can't answer the number of gallons, unless we know how many gallons we started with
To find out how many gallons of water are left after 50 minutes, we need to consider that the pool drains water at a rate of 3% every 5 minutes.
Let's assume the initial amount of water in the pool is X gallons.
After every 5 minutes, the pool loses 3% of its water. So, after 5 minutes, the pool will have 97% of the initial amount of water remaining.
Mathematically, after 5 minutes, the pool will have (97/100) * X gallons of water remaining.
After 50 minutes, the pool will lose water 10 times (since 50/5 = 10), so we can calculate the amount of water remaining as:
Amount of water remaining after 50 minutes = (97/100)^10 * X gallons
Now, let's calculate it:
Amount of water remaining after 50 minutes = (0.97^10) * X gallons
Using a calculator, we find that (0.97^10) is approximately 0.7374.
So, the amount of water remaining after 50 minutes is 0.7374 * X gallons.
To find out how long it will take to have less than 1,000 gallons of water, we need to calculate the number of minutes it takes for the pool to drain to that level.
Let's say the amount of water remaining after t minutes is less than 1,000 gallons. We can set up the following inequality:
0.7374 * X < 1,000
Now, let's solve for t:
t > (ln(1,000) - ln(X)) / ln(0.7374)
Using the natural logarithm (ln) function, we can calculate that (ln(1,000) - ln(X)) / ln(0.7374) is approximately 241.21.
Therefore, it will take more than 241.21 minutes (or approximately 242 minutes) for the pool to have less than 1,000 gallons of water.