Welcome to speed math! Speed tells us how fast something moves. The basic formula is Speed equals Distance divided by Time. We can rearrange this formula to find distance or time. The speed triangle helps us remember these relationships - just cover what you want to find! Common units include kilometers per hour for speed, and meters or kilometers for distance.
Let's solve a basic speed problem step by step. A car travels 120 kilometers in 2 hours. What is its speed? First, we identify what we know: distance is 120 km and time is 2 hours. We want to find speed, so we cover S in our triangle. This shows us to use distance divided by time. Speed equals 120 divided by 2, which equals 60 kilometers per hour. We can verify this by rearranging the formula to check our other values.
Average speed is not the same as the average of different speeds! Instead, average speed equals total distance divided by total time. Let's see an example. John walks 3 kilometers in 30 minutes, then runs 2 kilometers in 10 minutes. To find his average speed, we add the distances: 3 plus 2 equals 5 kilometers total. We add the times: 30 plus 10 equals 40 minutes total. Average speed is 5 divided by 40, which equals 7.5 kilometers per hour.
In meeting problems, two objects move toward each other. Their speeds add up! Amy and Ben start 10 kilometers apart. Amy walks at 4 kilometers per hour, Ben at 6 kilometers per hour. Their combined speed is 4 plus 6 equals 10 kilometers per hour. To cover 10 kilometers at 10 kilometers per hour takes exactly 1 hour. Let's watch them meet! Amy travels 4 kilometers and Ben travels 6 kilometers, totaling 10 kilometers.
Speed and time have an inverse relationship when distance stays constant. If speed increases, time decreases, and vice versa. Let's solve an example: A journey takes 3 hours at 60 kilometers per hour. How long at 80 kilometers per hour? First, find the distance: 60 times 3 equals 180 kilometers. At 80 kilometers per hour, time equals 180 divided by 80, which is 2.25 hours or 2 hours 15 minutes. The graph shows this inverse relationship as a curve.