Let's solve a classic meeting point problem. Two people A and B start from opposite ends of a road and walk toward each other. They meet after 4 hours at a point that is 4 kilometers away from the midpoint of the road. Our goal is to find the difference between their walking speeds.
Now let's analyze the distance relationship. When two people meet at a point 4 kilometers from the midpoint, it means that person A has walked 4 kilometers more than person B. This is because if they had walked the same distance, they would have met exactly at the midpoint. Since they met 4 kilometers past the midpoint toward B's starting position, A must have covered this extra 4 kilometers.
Let's derive this mathematically. If the total distance between A and B is D, and they meet at a point 4 kilometers past the midpoint, then person A walks a distance of D over 2 plus 4 kilometers, while person B walks D over 2 minus 4 kilometers. The difference between their distances is D over 2 plus 4, minus D over 2 minus 4, which equals 8 kilometers. So A walks exactly 8 kilometers more than B.
Now we can calculate the speed difference. We know that person A walks 8 kilometers more than person B in 4 hours. Using the formula for speed difference, we divide the distance difference by the time taken. So the speed difference equals 8 kilometers divided by 4 hours, which gives us 2 kilometers per hour. Therefore, person A walks 2 kilometers per hour faster than person B.