\[ \frac{d}{60} + \frac{d}{40} = 5 \]

["Solving the Equation (\dfrac{d}{60} + \dfrac{d}{40} = 5): A Quick Guide", "Understanding how to solve equations like (\dfrac{d}{60} + \dfrac{d}{40} = 5) is essential for students, teachers, and anyone tackling algebra. This type of equation appears frequently in math problems involving rates, work, or proportional reasoning. In this article, we’ll walk through step-by-step how to solve (\dfrac{d}{60} + \dfrac{d}{40} = 5), explain the concepts clearly, and highlight how it can appear in real-world scenarios.", "---", "### What Is the Equation (\dfrac{d}{60} + \dfrac{d}{40} = 5)?", "This equation models a situation where two rates are combined—specifically, two fractions of a quantity (d) divided over different intervals or rates (60 and 40). Solving it involves finding the value of (d) that satisfies the total of 5.", "---", "### Step 1: Combine the Fractions", "Before solving, simplify the left-hand side by adding the two fractions:", "[\n\dfrac{d}{60} + \dfrac{d}{40} = 5\n]", "To combine these, find a common denominator. The least common multiple (LCM) of 60 and 40 is 120.", "Rewriting each fraction with denominator 120:", "[\n\dfrac{d}{60} = \dfrac{2d}{120}, \quad \dfrac{d}{40} = \dfrac{3d}{120}\n]", "So the equation becomes:", "[\n\dfrac{2d}{120} + \dfrac{3d}{120} = \dfrac{5d}{120} = 5\n]", "---", "### Step 2: Solve for (d)", "Now simplify:", "[\n\dfrac{5d}{120} = 5\n]", "Multiply both sides by 120 to eliminate the denominator:", "[\n5d = 600\n]", "Then divide both sides by 5:", "[\nd = 120\n]", "---", "### ✅ Final Answer:", "[\n\boxed{d = 120}\n]", "This means that when (d = 120), the sum (\dfrac{120}{60} + \dfrac{120}{40} = 2 + 3 = 5), satisfying the equation perfectly.", "---", "### Real-World Applications", "Equations like this appear in:", "- Rate problems: If two workers complete tasks at different speeds (e.g., Worker A at 1/60 tasks per minute, Worker B at 1/40), combined they finish a certain total. The variable (d) represents total work, and solving finds how much work corresponds to a target completion time.", "- Physics and engineering: Calculating time, distance, or rate relationships where multiple inputs contribute additively.", "- Finance and budgeting: Combining interest rates or expense breakdowns over time.", "---", "### Tips for Solving Similar Equations", "- Always find a common denominator before adding fractions.\n- Simplify all fractions to standardize.\n- Isolate the variable after combining terms.\n- Multiply through by denominators to eliminate fractions completely.\n- Check your answer by plugging (d) back into the original equation.", "---", "### Why This Equation Matters", "Mastering equations like (\dfrac{d}{60} + \dfrac{d}{40} = 5) strengthens foundational algebra skills—skills essential for advanced math, science, and everyday problem-solving. Whether you're preparing for standardized tests or working on real-life calculations, understanding how to combine and solve fractional rates empowers smarter decision-making.", "---", "### Related Keywords for SEO", "- Solve (\dfrac{d}{60} + \dfrac{d}{40} = 5)\n- Algebra equation solution step-by-step\n- Combining fractions in algebra\n- Word problems with rates\n- Step-by-step math tutorial\n- Practice solving linear equations\n- Common denominator algebra\n- Real-world rate problems", "---", "By breaking down the equation clearly and connecting it to practical use, learners gain both confidence and competence in algebra. The answer, (\dfrac{d}{60} + \dfrac{d}{40} = 5) simplifies neatly to (d = 120)—a satisfying resolution rooted in logical math."]