Question

STEM Lucy is sailing in a race. She reaches the quarter mile buoy at 1:30 p.m.

At 1:36 p.m., she reaches the mile buoy. Use this information to determine her
average rate of change, in miles per minute.

Answer 1

Step-by-step explanation;

To determine Lucy's average rate of change in miles per minute, we need to calculate the total distance she covered and the total time it took her to cover that distance.

Given that Lucy reached the quarter mile buoy at 1:30 p.m. and the mile buoy at 1:36 p.m., we can calculate the time difference between the two points:

1:36 p.m. - 1:30 p.m. = 6 minutes

Since she covered the distance from the quarter mile buoy to the mile buoy, which is 3/4 mile, we can calculate her average rate of change by dividing the distance by the time:

3/4 mile / 6 minutes = 1/4 mile per minute

Therefore, Lucy's average rate of change, in miles per minute, is 1/4 mile per minute.

To further illustrate this, if Lucy were to maintain this rate of change, she would cover 1/4 mile every minute. So, after 2 minutes, she would have covered 1/2 mile, and after 4 minutes, she would have covered 1 mile.

Keep in mind that this calculation assumes Lucy traveled at a constant speed between the two buoys. If her speed varied, this average rate of change may not accurately represent her overall speed.

Answer 2

Lucy's average rate of change, or average speed, for the sailing race is 1/8 mile per minute.

To calculate Lucy's average rate of change, which in this context is her average speed, we need to use the distance she traveled and the time it took for her to travel that distance. In this case, Lucy traveled the difference between the quarter mile buoy and the mile buoy in 6 minutes, which is the time interval from 1:30 p.m. to 1:36 p.m.

First, we need to determine the distance traveled. Since she reached the quarter mile buoy and then the mile buoy, she traveled 1 mile - 1/4 mile = 3/4 mile.

Next, we convert the time from minutes to hours to calculate her speed in miles per minute. There are 6 minutes to be considered. To find the average speed, we use the formula:

Average Speed = Total Distance / Total Time

Average Speed = (3/4 mile) / (6 minutes)

Average Speed = 1/8 mile per minute

Therefore, Lucy's average rate of change is 1/8 mile per minute.