Question

This should be simple I know, I just CAN'T FIGURE IT OUT

A pool drains at a rate of 3% every 5 minutes. If it starts with 1500 gallons, how many gallons are left in the pool after 50 minutes? About how many minutes will it take to have less than 1000 gallons in the pool? Justify your answer with a mathematical model of the problem situation.

Answer 1

A. 1050 gallons

B. 56 minutes (55.56 minutes)

Explanation:

3% is .03. If it drains .03 every 5 minutes, that means it drains .006 every minute (.03/5).

.6% of 1500 is 9. That means it drains 9 gallons per minute. (.006 * 1500). Draining means the 9 is negative.

x is time, y is gallons

y= -9x + 1500. substitute 50 for x

y= -9(50) + 1500

y= 1050

After 50 minutes, there are 1050 gallons in the pool.

Now to find when y<1000, substitute 1000 for y and solve for x to find time.

1000 < -9x + 1500. Subtract 1500 from both sides

-500< -9x. Divide by -9

FLIP the inequality when dividing

by a negative number!

55.56> x

It will take about 56 minutes to have less than 1000 gallons in the pool.