Question

Marcus has a pool that can hold a maximum of 4500 gallons of water. The pool already contains 1500 gallons of water. Marcus begins to add more water at a rate of 30 gallons per minute. Enter an inequality that shows the number of minutes , m, Marcus can continue to add water to the pool without exceeding the maximum number of gallons

Answer 1

Since the rate of change or the rate at which the pool gets filled up is 30 grams per minute we could say that it fills up in 30(m) since it already has 1500g in the pool and the maximum amount of water it could hold is 4500 so the amount of water that must be at the pool after m minutes is less than or equal to 4500. Therefore the equation will look like this

`30m+1500 \leq 4500`
if you solve the inequality you will have that


`30m+1500 \leq 4500 30m \leq 3000 m \leq 100`

In other words, it will take at the most 100 minutes for the pool to fill up to 4500