Michael spends a half-hour adding water to his pool, part of the art the rate of 15 gallons per minute and the rest of the time at the rate of 9 gallons per minute. Let t be the time in minutes that he adds water at the faster rate. Enter an algebraic expression to represent the total amount of water added to the pool. 

To represent the total amount of water added to the pool, let's break down the problem:

1. **Time spent at the faster rate (15 gallons per minute):**  
   This is given as \( t \) minutes.  
   The amount of water added during this time is \( 15t \) gallons.

2. **Time spent at the slower rate (9 gallons per minute):**  
   Since Michael spends a half-hour (which is 30 minutes in total) adding water, the time spent at the slower rate is \( 30 - t \) minutes.  
   The amount of water added during this time is \( 9(30 - t) \) gallons.

To find the total amount of water added to the pool, sum the water added during both periods:

\[
\text{Total water added} = 15t + 9(30 - t)
\]

This is the algebraic expression representing the total amount of water added to the pool.

Would you like to simplify the expression further or need additional details on this? Here are 5 related questions you might consider:

1. What is the simplified form of the total water expression?
2. How much water is added if Michael spends 10 minutes at the faster rate?
3. How would the expression change if the total time was 1 hour instead of 30 minutes?
4. What if the rate for the slower period was different?
5. Can you represent the total water added as a function of \( t \) only?

**Tip:** Always check the units of time and rate to ensure consistency when setting up algebraic expressions.

Understand how to calculate the total amount of water added to Michael's pool based on different rates of water addition. This problem involves algebraic expressions and rates of work, covering both faster and slower water addition rates. Suitable for Grades 7-9 students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation