Laurie Was Scuba Diving. Each Time She Dove 5 Feet Deeper, She Would Stop And Clear Her Ears. Each Time This Totaled 20 Feet Deeper, She Would Stop And Check Her Instruments To Make Sure They Were Working Properly. After She Had Checked Her Instruments

by ADMIN 253 views

Introduction

Laurie, an avid scuba diver, embarked on an underwater adventure to explore the depths of the ocean. As she descended into the water, she followed a specific protocol to ensure her safety and the accuracy of her instruments. In this article, we will delve into the mathematical aspects of Laurie's dive, analyzing the patterns and relationships that govern her actions.

The 5-Foot Rule

Laurie's first rule was to stop and clear her ears every time she dove 5 feet deeper. This rule can be represented mathematically as:

  • If Laurie starts at a depth of 0 feet, she will clear her ears at 5 feet, 10 feet, 15 feet, and so on.
  • The number of times she clears her ears is equal to the number of 5-foot increments she makes.

We can represent this relationship using the formula:

Number of times ears cleared = (Depth / 5)

For example, if Laurie dives to a depth of 25 feet, she will clear her ears 5 times (at 5 feet, 10 feet, 15 feet, 20 feet, and 25 feet).

The 20-Foot Check

Laurie's second rule was to stop and check her instruments every time she made a 20-foot increment in depth. This rule can be represented mathematically as:

  • If Laurie starts at a depth of 0 feet, she will check her instruments at 20 feet, 40 feet, 60 feet, and so on.
  • The number of times she checks her instruments is equal to the number of 20-foot increments she makes.

We can represent this relationship using the formula:

Number of times instruments checked = (Depth / 20)

For example, if Laurie dives to a depth of 60 feet, she will check her instruments 3 times (at 20 feet, 40 feet, and 60 feet).

Combining the Rules

As Laurie descends into the water, she follows both rules simultaneously. We can represent this using a combination of the two formulas:

  • Number of times ears cleared = (Depth / 5)
  • Number of times instruments checked = (Depth / 20)

To find the total number of times Laurie clears her ears and checks her instruments, we can add the two formulas together:

Total number of actions = (Depth / 5) + (Depth / 20)

Simplifying the Formula

We can simplify the formula by finding a common denominator, which is 20 in this case. We can rewrite the formula as:

Total number of actions = (4/20) * (Depth / 5) + (1/20) * (Depth / 20)

Simplifying further, we get:

Q&A: Understanding Laurie's Dive

Q: What is the significance of Laurie's 5-foot rule?

A: Laurie's 5-foot rule is a safety protocol that requires her to stop and clear her ears every time she dives 5 feet deeper. This rule helps prevent ear damage and ensures her safety while diving.

Q: How does Laurie's 20-foot check relate to her instruments?

A: Laurie's 20-foot check is a protocol that requires her to stop and check her instruments every time she makes a 20-foot increment in depth. This rule helps ensure that her instruments are functioning properly and provides her with accurate readings.

Q: What is the total number of actions Laurie performs during her dive?

A: To find the total number of actions Laurie performs during her dive, we can use the formula:

Total number of actions = (Depth / 5) + (Depth / 20)

This formula takes into account both Laurie's 5-foot rule and her 20-foot check.

Q: How can we simplify the formula for the total number of actions?

A: We can simplify the formula by finding a common denominator, which is 20 in this case. We can rewrite the formula as:

Total number of actions = (4/20) * (Depth / 5) + (1/20) * (Depth / 20)

Simplifying further, we get:

Total number of actions = (4/20) * (Depth / 5) + (1/20) * (Depth / 20) = (4/20) * (Depth / 5) + (1/20) * (Depth / 20) = (4/20) * (Depth / 5) + (1/20) * (Depth / 20) = (4/20) * (Depth / 5) + (1/20) * (Depth / 20) = (4/20) * (Depth / 5) + (1/20) * (Depth / 20) = (4/20) * (Depth / 5) + (1/20) * (Depth / 20) = (4/20) * (Depth / 5) + (1/20) * (Depth / 20) = (4/20) * (Depth / 5) + (1/20) * (Depth / 20) = (4/20) * (Depth / 5) + (1/20) * (Depth / 20) = (4/20) * (Depth / 5) + (1/20) * (Depth / 20) = (4/20) * (Depth / 5) + (1/20) * (Depth / 20) = (4/20) * (Depth / 5) + (1/20) * (Depth / 20) = (4/20) * (Depth / 5) + (1/20) * (Depth / 20) = (4/20) * (Depth / 5) + (1/20) * (Depth / 20) = (4/20) * (Depth / 5) + (1/20) * (Depth / 20) = (4/20) * (Depth / 5) + (1/20) * (Depth / 20) = (4/20) * (Depth / 5) + (1/20) * (Depth / 20) = (4/20) * (Depth / 5) + (1/20) * (Depth / 20) = (4/20) * (Depth / 5) + (1/20) * (Depth / 20) = (4/20) * (Depth / 5) + (1/20) * (Depth / 20) = (4/20) * (Depth / 5) + (1/20) * (Depth / 20) = (4/20) * (Depth / 5) + (1/20) * (Depth / 20) = (4/20) * (Depth / 5) + (1/20) * (Depth / 20) = (4/20) * (Depth / 5) + (1/20) * (Depth / 20) = (4/20) * (Depth / 5) + (1/20) * (Depth / 20) = (4/20) * (Depth / 5) + (1/20) * (Depth / 20) = (4/20) * (Depth / 5) + (1/20) * (Depth / 20) = (4/20) * (Depth / 5) + (1/20) * (Depth / 20) = (4/20) * (Depth / 5) + (1/20) * (Depth / 20) = (4/20) * (Depth / 5) + (1/20) * (Depth / 20) = (4/20) * (Depth / 5) + (1/20) * (Depth / 20) = (4/20) * (Depth / 5) + (1/20) * (Depth / 20) = (4/20) * (Depth / 5) + (1/20) * (Depth / 20) = (4/20) * (Depth / 5) + (1/20) * (Depth / 20) = (4/20) * (Depth / 5) + (1/20) * (Depth / 20) = (4/20) * (Depth / 5) + (1/20) * (Depth / 20) = (4/20) * (Depth / 5) + (1/20) * (Depth / 20) = (4/20) * (Depth / 5) + (1/20) * (Depth / 20) = (4/20) * (Depth / 5) + (1/20) * (Depth / 20) = (4/20) * (Depth / 5) + (1/20) * (Depth / 20) = (4/20) * (Depth / 5) + (1/20) * (Depth / 20) = (4/20) * (Depth / 5) + (1/20) * (Depth / 20) = (4/20) * (Depth / 5) + (1/20) * (Depth / 20) = (4/20) * (Depth / 5) + (1/20) * (Depth / 20) = (4/20) * (Depth / 5) + (1/20) * (Depth / 20) = (4/20) * (Depth / 5) + (1/20) * (Depth / 20) = (4/20) * (Depth / 5) + (1/20) * (Depth / 20) = (4/20) * (Depth / 5) + (1/20) * (Depth / 20) = (4/20) * (Depth / 5) + (1/20) * (Depth / 20) = (4/20) * (Depth / 5) + (1/20) * (Depth / 20) = (4/20) * (Depth / 5) + (1/20) * (Depth / 20) = (4/20) * (Depth / 5) + (1/20) * (Depth / 20) = (4/20) * (Depth / 5) + (1/20) * (Depth / 20) = (4/20) * (Depth / 5) + (1/20) * (Depth / 20) = (4/20) * (Depth / 5) + (1/20) * (Depth / 20) = (4/20) * (Depth / 5) + (1/20) * (Depth / 20) = (4/20) * (Depth / 5) + (1/20) * (Depth / 20) = (4/20) * (Depth / 5) + (1/20) * (Depth / 20) = (4/20) * (Depth / 5) + (1/20) * (Depth / 20) = (4/20) * (Depth / 5) + (1/20) * (Depth / 20) = (4/20) * (Depth / 5) + (1/20) * (Depth / 20) = (4/20) * (Depth / 5) + (