Understanding Constant Rate and Proportionality

The video tutorial explains how to derive an equation representing the relationship between distance and time for a runner, Justin, who runs at a constant rate. It begins by introducing the problem, then sets up an equation using a constant rate. The tutorial proceeds to solve for the constant using given data and concludes by presenting the final equation with units.

What is the total distance Justin covers in 2 hours?

• 25 kilometers

• 15 kilometers

• 17 kilometers

• 20 kilometers

What does the constant rate imply in terms of distance and time?

• Distance is inversely proportional to time

• Distance is directly proportional to time

• Distance is unrelated to time

• Distance decreases as time increases

What symbol is used to represent the constant of proportionality?

• r

• k

• m

• c

How do you calculate the constant k using the given data?

• Add distance and time

• Subtract time from distance

• Divide distance by time

• Multiply distance by time

What is the value of k in this scenario?

• 9 kilometers per hour

• 8.5 kilometers per hour

• 8 kilometers per hour

• 9.5 kilometers per hour

What is the equation that represents the relationship between distance and time?

• d = 8.5 + h

• d = 8.5 / h

• d = 8.5 - h

• d = 8.5 * h

What does the equation d = 8.5 * h represent?

• Distance is constant regardless of time

• Distance decreases by 8.5 kilometers every hour

• Distance increases by 8.5 kilometers every hour

• Distance decreases as time increases

What units are used for the constant k in the equation?

• Kilometers per hour

• Miles per hour

• Kilometers per minute

• Meters per second

Why is it important to include units in the final equation?

• To make the equation longer

• To confuse the reader

• To ensure clarity and accuracy

• To make the equation look complex

If Justin runs for 3 hours, how far will he have traveled?

• 26 kilometers

• 24 kilometers

• 27 kilometers

• 25.5 kilometers