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Interpret speed as a rate

Speed describes the distance traveled for each one unit of time, so a ratio such as 120 miles in 3 hours represents a unit rate of 40 miles per hour. Tables, double number lines, and coordinate graphs can show equivalent distance–time relationships and support comparisons, while emphasizing that greater distance does not necessarily mean greater speed unless the time is also considered. This scope treats speed as a constant or overall rate and excludes instantaneous speed, velocity, and acceleration.

Detailed Explanation: Interpret speed as a rate

Speed tells how much distance is traveled in 1 unit of time. To find speed, divide:

speed=distancetime\text{speed}=\frac{\text{distance}}{\text{time}}

The answer should include units, such as miles per hour.

Example:
Car A travels 120120 miles in 33 hours. Car B travels 150150 miles in 55 hours. Which car is faster?

Step 1: Find Car A’s speed.

120 miles3 hours=40 miles per hour\frac{120\text{ miles}}{3\text{ hours}}=40\text{ miles per hour}

Car A travels 4040 miles for every 11 hour.

Step 2: Find Car B’s speed.

150 miles5 hours=30 miles per hour\frac{150\text{ miles}}{5\text{ hours}}=30\text{ miles per hour}

Car B travels 3030 miles for every 11 hour.

Step 3: Compare the unit rates.

40 miles per hour>30 miles per hour40\text{ miles per hour}>30\text{ miles per hour}

So, Car A is faster.

Notice that Car B traveled a greater total distance, but it took more time. To compare speed fairly, compare the distance traveled for 1 hour, not just the total distance.

Learn by doing: Interpret speed as a rate

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Speed - Distance and Time to Speed - Same Units


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