Problem 26 - Basic Engineering Mathematics

Question

It takes 50 minutes to machine a certain part. Using a new type of tool, the time can be reduced by \(15 \%\). Calculate the new time taken.

Step-by-Step Solution

Answer

The new time is 42.5 minutes.

Step 1: Understand the Reduction Percentage

The problem states that the manufacturing time can be reduced by 15%. This means the new time is 85% of the original time because we take away 15% of it.

Step 2: Calculate 15% of Original Time

First, find out what 15% of the original 50 minutes is. We calculate this by multiplying 50 minutes by 15% (or 0.15 in decimal form): \[15\% \text{ of } 50 = 50 \times 0.15 = 7.5 \text{ minutes}\]

Step 3: Subtract the Reduction from Original Time

Subtract the 7.5 minutes (the time reduction) from the original 50 minutes to find the new time it takes:\[50 - 7.5 = 42.5 \text{ minutes}\]

Key Concepts

Time Reduction Insight

When we talk about time reduction, especially in an industrial or engineering context, it means finding ways to make tasks faster. This can be hugely beneficial. Imagine running a machine for less time. It saves energy and increases efficiency. If machining a part takes 50 minutes and you manage to cut 15% off, that's significant. How do we understand this? By realizing that reducing time by 15% will take away 15% from the total time needed. You start with 100% of the original time (50 minutes), then subtract 15%. This leaves you with 85% of the original time, and you'll find that calculating 85% of something makes the task quicker.

Role of Engineering Mathematics

Engineering mathematics plays a crucial role in solving real-world problems. This problem is an example of applying math to improve industrial processes. Engineers often use precise calculations like this to optimize efficiency and reduce costs. By calculating percentages and reductions, they can design tools and processes that make operations quicker and cheaper. Applying this knowledge, in this case, led to understanding how much time was saved. Using mathematical formulas ensures accuracy and helps engineers quantify improvements in terms of time and costs, leading to better decision-making.

Mastering Decimal Conversion

Decimal conversion is an essential skill in engineering and mathematics. It allows us to switch between different forms of representing numbers easily. For example, in the original problem, knowing that 15% equates to 0.15 is critical. This simple conversion lets you multiply the original time with the percentage and easily find the reduced time. This skill makes complex problems easier to manage as it allows engineers and students alike to perform calculations involving percentages swiftly. Mastering decimal conversion thus provides a strong foundation for solving a wide range of mathematical problems efficiently.