Problem 94 - Elementary and Intermediate Algebra

Question

Submarines. A submarine was cruising at a depth of \(1,250\) feet. The captain gave the order to climb 550 feet. Compared to sea level, find the new depth of the sub.

Step-by-Step Solution

Answer

The submarine's new depth is 700 feet below sea level.

Step 1: Understand the Initial Depth

The submarine is initially at a depth of 1,250 feet, meaning it is 1,250 feet below sea level.

Step 2: Identify the Climb

The captain orders the submarine to climb 550 feet, which means moving 550 feet closer to sea level.

Step 3: Calculate the Change in Depth

To find the submarine's new depth, subtract the climb from the initial depth: \[ 1,250 - 550 = 700 \] feet. This calculation shows the new depth relative to sea level.

Key Concepts

Understanding Depth Calculation in Submarine Navigation

Depth calculation is an essential skill in submarine navigation and other underwater explorations. When dealing with depths, we often refer to the distance below sea level. Here, understanding the appropriate use of subtraction is crucial.

For the submarine exercise, the depth was initially determined as 1,250 feet below sea level. When we receive a command like climbing, which suggests moving upwards, we need to adjust this depth to find a new measurement. This involves a generalized concept where:

• The starting depth is known or measured.
• An adjustment (like climbing or descending) is applied.
• A final depth is calculated after applying the adjustment.

In math terms, when the submarine climbs, the total depth decreases, and we perform a subtraction operation to find the new depth. This method is essential in ensuring that submarines maintain safe operational levels under varying oceanic conditions.

Subtraction in Context: Adjusting Depth

Subtraction is widely used in various practical contexts, such as finding the new depth of a submarine. In word problems or real-world applications like this, it's important to interpret what subtraction means.

In our scenario, the submarine starts 1,250 feet below sea level and is ordered to climb 550 feet. Here, "climb" implies a reduction in depth, so subtraction comes into play.

• Identify the initial condition: Start at 1,250 feet below.
• Determine what needs to be subtracted: 550 feet (the climb).
• Perform the subtraction: \[1,250 - 550 = 700\] feet, giving the new position relative to sea level.

This shows how subtraction helps adjust measurements, ensuring an accurate understanding of the current situation. Similar skills apply to everyday situations, like budgeting or calculating time remaining for an activity.

Applying Math to Real-World Scenarios

Mathematics isn't just for abstract theory; it's highly applicable in real-world situations. Problems like our submarine depth adjustment teach critical skills that can be broadly applied.

Working with numbers in real-life contexts involves:

• Identifying the problem or starting situation, as with the initial submarine depth.
• Understanding numerical changes in the scenario, such as climbing towards sea level.
• Executing mathematical operations to describe the new condition effectively.

For instance, sailors and navigators routinely use these skills to maintain safe operation standards. Similarly, you might use similar principles when measuring how much space you have left in storage or tracking marathon progress over distances.

Through exercises like these, students learn to apply mathematical reasoning to a variety of fields—highlighting the functionality and versatility of math in diverse real-world situations.