Lesson 5: Speed

Property

Speed acts as a conversion factor between distance and time units: $\text{speed} = \frac{\text{distance}}{\text{time}}$ allows conversion from time to distance or distance to time.

Examples

Property

For an object moving in at a uniform (constant) rate, the distance traveled, the elapsed time, and the rate are related by the formula

where $d =$ distance, $r =$ rate, and $t =$ time.

Examples

• A cyclist travels at a steady rate of 15 miles per hour for 4 hours. The total distance is $d = 15 \cdot 4 = 60$ miles.

• A bus covers a distance of 120 miles in 2 hours. Its average rate of speed is $r = \frac{120}{2} = 60$ miles per hour.

Property

When two objects start at the same point and travel in opposite directions, the distance between them is the sum of the distances each object has traveled.

Formula:

Examples

• Two cars leave a gas station at the same time, one heading east at 60 mph and the other west at 70 mph. To find when they are 325 miles apart, solve $60t + 70t = 325$. It takes 2.5 hours.
• Cindy rides her bike north at 15 mph, and Richard rides south at 12 mph. They start from their dorm at the same time. The time it takes for them to be 54 miles apart is found by solving $15t + 12t = 54$, which gives $t = 2$ hours.
• Two jets leave from the same airport. One flies north at 500 mph and the other flies south at 550 mph. After 3 hours, the distance between them is $(500)(3) + (550)(3) = 1500 + 1650 = 3150$ miles.