A runner charted how long it took her to run certain distances. Here is the information she gathered:
Minutes
Miles
0
0
8
1
16
2
24
3
At this pace, how long will it take her to run 5 miles?
To find out how long it will take her to run 5 miles, we'll first need to determine the rate at which she is running. We can do this by finding the slope of the line that connects two of the known points on the chart.
Let's choose the points (0,0) and (8,1).
The slope of a line is given by the formula:
slope = (change in y) / (change in x)
In this case, the change in y is 1 - 0 = 1, and the change in x is 8 - 0 = 8.
So the slope of the line connecting these two points is 1/8.
Now we can use this slope to determine how many minutes it will take her to run 5 miles.
To do this, we'll first find the rate at which she is running, in miles per minute. The rate is equal to the reciprocal of the slope, since the slope = (change in y) / (change in x) = (1/8).
So the rate is 8/1 = 8 miles per minute.
Finally, we can calculate the time it will take her to run 5 miles.
Time = distance / rate
Time = 5 miles / 8 miles per minute
Time = 5/8 minutes
Therefore, it will take her 5/8 minutes to run 5 miles.