Find the rate of change for the situation: You run 3 miles in one hour and 6 miles in two hours.
The rate of change of a quantity is defined as the speed of change that the quantity undergoes in a given duration of time. For example, speed is known as the rate of change of position.
Answer: The rate of change for the situation given is 3 miles per hour.
Let's understand the solution in detail.
Let's visualize the problem in coordinates (u, v).
Let u be the distance covered in miles and v be the corresponding time in hours.
So, now, we have the pairs (1, 3) and (2, 6) as given in the situation.
Now, we calculate the slope using the slope formula; which will give us the rate of change of the situation.
⇒ m = (6 - 3) miles / (2 - 1) hour = 3 miles / 1 hour = 3 miles / hour