twelve posts stand equidistant along the stadium. starting at the first post, a runner reaches the eight post in 8 seconds. if he runs at a constant rate, how many seconds are needed to reach the twelfth post?
To move the seven post-to-post distances (1 to 8) requires 8 seconds. That is 8/7 sesonds per interval. To run 4 more intervals at the same speed requires 4* 8/7 = 4.57 s more time, for a total (from the beginning) of 12.57 s
To solve this problem, we can assume that the distance between each post is equal.
Since the runner reaches the 8th post in 8 seconds and all posts are equidistant, this means that the runner takes 1 second to move from one post to the next.
To find out how many seconds are needed to reach the 12th post, we can subtract the initial time taken to reach the 8th post (8 seconds) from the total time needed to reach the 12th post.
The total time needed to reach the 12th post can be calculated by multiplying the number of posts between the 8th and 12th by the time it takes to move from one post to the next (1 second).
Number of posts between the 8th and 12th post: 12 - 8 = 4 posts
Total time needed to reach the 12th post: 4 posts * 1 second/post = 4 seconds
Therefore, it will take 4 seconds to reach the 12th post.
To solve this problem, we need to first determine the distance between each post. Since the posts are equidistant, we can calculate the distance by dividing the total distance from the first post to the eighth post by the number of intervals between the posts.
Given that the runner reaches the eighth post in 8 seconds and assuming he maintains a constant rate, we can determine that the eighth post is 8 intervals away from the first post.
Let's denote the distance between each post as "d" and the number of intervals between the first and eighth post as "n". We can use the formula:
Distance = Speed × Time
In this case, the distance between the first and eighth post is equal to the speed of the runner multiplied by the time it takes to cover that distance, which is 8 intervals:
d × n = 8
Since the posts are equidistant, we can determine that the distance between each post, "d," is equal to the total distance covered by the runner divided by the number of intervals:
d = Total Distance / Number of Intervals
Substituting the values we know, we can calculate the distance between each post:
d = 8 / 8 = 1
Now that we know the distance between each post is 1 interval, we can determine the time it takes to reach the twelfth post by multiplying the distance (1 interval) by the number of intervals (12):
Time = Distance × Number of Intervals
Time = 1 interval × 12 = 12 seconds
Therefore, it would take the runner 12 seconds to reach the twelfth post at a constant rate.