A woman can bicycle 20 miles in the same time as it takes her to walk 4 miles. She can ride 8 mph faster than she can walk. How fast can she walk? mph

Let's dive into the numbers! If we let the woman's walking speed be \( x \) mph, then her cycling speed would be \( x + 8 \) mph. The time taken to walk 4 miles is \( \frac{4}{x} \) hours, and the time taken to bicycle 20 miles is \( \frac{20}{x + 8} \) hours. Since these two times are equal, we can set up the equation: \[ \frac{4}{x} = \frac{20}{x + 8} \] Cross-multiplying gives us: \[ 4(x + 8) = 20x \] This simplifies to: \[ 4x + 32 = 20x \] Bringing all terms involving \( x \) on one side: \[ 32 = 20x - 4x \] \[ 32 = 16x \] \[ x = 2 \] So, she can walk at a speed of 2 mph! Now, let's talk about real-world applications! Knowing these speeds can be quite useful for planning your daily activities—like choosing whether to bike or walk based on your time constraints. If you're late, biking is the clear winner! Plus, this information can help you gauge how long it’ll take to enjoy scenic routes or leisurely strolls without over-exerting yourself. Another neat aspect is the problem-solving approach! Always double-check your setup and simplify wherever possible to avoid mistakes. A common pitfall is overlooking the relationship between the speeds—make sure to define your variables clearly. With practice, you'll become a speed solver in no time!