According to the problem, \(\frac{d}{60} + \frac{d}{40} = 5\).

["Solving the Equation: How to Solve (\frac{d}{60} + \frac{d}{40} = 5) Step-by-Step", "Understanding and solving equations like (\frac{d}{60} + \frac{d}{40} = 5) is essential for students and professionals alike, especially when dealing with rate problems or work-time problems. In this SEO-optimized article, we’ll explore how to solve the equation (\frac{d}{60} + \frac{d}{40} = 5), explain its real-world applications, and highlight key mathematical concepts to boost your problem-solving skills.", "---", "### Understanding the Equation", "The equation (\frac{d}{60} + \frac{d}{40} = 5) models a real-life scenario involving two quantities moving or working together at different rates. Specifically, it represents the combined rate of two tools or workers completing a task. Here, the variable (d) represents a shared quantity—like distance, time, or work output—divided by time (in minutes) to reflect rate.", "---", "### Step-by-Step Solution", "Let’s solve the equation step by step for (d):", "Step 1: Combine the fractions.\nBoth terms have (d) and denominators of 60 and 40. First, find a common denominator for the fractions. The least common multiple (LCM) of 60 and 40 is 120.", "[\n\frac{d}{60} = \frac{2d}{120}, \quad \frac{d}{40} = \frac{3d}{120}\n]", "So the equation becomes:", "[\n\frac{2d}{120} + \frac{3d}{120} = 5\n]", "Step 2: Add the fractions:", "[\n\frac{2d + 3d}{120} = 5 \quad \Rightarrow \quad \frac{5d}{120} = 5\n]", "Step 3: Simplify the fraction:", "[\n\frac{d}{24} = 5\n]", "Step 4: Solve for (d) by multiplying both sides by 24:", "[\nd = 5 \ imes 24 = 120\n]", "---", "### Final Answer", "[\n\boxed{d = 120}\n]", "This means that under the given conditions, the value of (d) must be 120 for the equation to hold true.", "---", "### Real-World Applications", "This type of equation applies to various practical situations, including:", "- Work problems: If two workers collaborate at different speeds, combined rates help determine work completion time.\n- Physics and motion: When objects move toward each other (or add distances), summing rates equates total progress over time.\n- Flow rates: In plumbing or chemistry, flow or reaction rates can be combined similarly.", "---", "### Key Takeaways", "- Always find a common denominator when combining fractions with variables.\n- Simplify carefully and isolate the variable using inverse operations.\n- This equation exemplifies how rate, time, and distance/work are interrelated.", "---", "### Want to Improve Your Equation-Solving Skills?", "Mastering equations like (\frac{d}{60} + \frac{d}{40} = 5) strengthens your algebraic foundation. For more practice problems, explore similar rate and work equations and consider applying these methods to real-world scenarios—like budgeting time, calculating fuel efficiency, or optimizing team productivity.", "---", "Keywords: (\frac{d}{60} + \frac{d}{40} = 5), equation solving, algebra tutorial, work rate problem, rate equation, math problem solving, fractional equations", "Meta description: Learn how to solve (\frac{d}{60} + \frac{d}{40} = 5) step-by-step with clear explanation, real-world applications, and key math concepts for students and problem solvers. Boost your algebra skills today!"]