8.1: Back on the Treadmill Again
While training for a race, Andre’s dad ran 12 miles in 75 minutes on a treadmill. If he runs at that rate:
- How long would it take him to run 8 miles?
- How far could he run in 30 minutes?
Let’s investigate constant speed some more.
While training for a race, Andre’s dad ran 12 miles in 75 minutes on a treadmill. If he runs at that rate:
Kiran and Clare live 24 miles away from each other along a rail trail. One Saturday, the two friends started walking toward each other along the trail at 8:00 a.m. with a plan to have a picnic when they meet.
Kiran walks at a speed of 3 miles per hour while Clare walks 3.4 miles per hour.
Jada bikes 2 miles in 12 minutes. Jada’s cousin swims 1 mile in 24 minutes.
One day Jada and her cousin line up on the end of a swimming pier on the edge of a lake. At the same time, they start swimming and biking in opposite directions.
When two objects are each moving at a constant speed and their distance-to-time ratios are equivalent, we say that they are moving at the same speed. If their time-distance ratios are not equivalent, they are not moving at the same speed.
We describe speed in units of distance per unit of time, like miles per hour or meters per second.
We can also use pace to describe distance and time. We measure pace in units such as hours per mile or seconds per meter.
Speed and pace are reciprocals. Both can be used to compare whether one object is moving faster or slower than another object.
Because speed is a rate per 1 unit of time for ratios that relate distance and time, we can multiply the amount of time traveled by the speed to find the distance traveled.
time (minutes) | distance (centimeters) | |
---|---|---|
row 1 | 2 | 5 |
row 2 | 1 | 2.5 |
row 3 | 4 | $4 \boldcdot (2.5)$ |
Pace is an attribute that tells you how fast or slow an object is moving. A greater pace means the object is moving more slowly. Pace is measured in units like seconds per meter, hours per miles, and minutes per kilometer.
Speed is an attribute that tells you how fast or slow an object is moving. A greater speed means the object is moving faster. Speed is measured in units of distance per unit of time like meters per second, miles per hour, and kilometers per second.