In a 300 m race A beats B by 22.5 m or 6 seconds. B's time over the course is:86 sec80 sec76 sec70 secNone
Question
In a 300 m race A beats B by 22.5 m or 6 seconds. B's time over the course is:
- 86 sec
- 80 sec
- 76 sec
- 70 sec
- None
Solution
The problem states that A beats B by 22.5 meters or 6 seconds in a 300 meter race. This means that B runs 22.5 meters in the time that A runs 300 meters.
We can set up a proportion to solve for B's time over the course.
Let's denote B's time as T.
The proportion is:
300 meters / A's time = 22.5 meters / 6 seconds
We know that A's time is T - 6 seconds (since A finishes 6 seconds before B).
So, we can rewrite the proportion as:
300 meters / (T - 6 seconds) = 22.5 meters / 6 seconds
Cross-multiplying gives us:
300 meters * 6 seconds = 22.5 meters * (T - 6 seconds)
Solving for T gives us:
T = (300 meters * 6 seconds) / 22.5 meters + 6 seconds
T = 80 seconds
So, B's time over the course is 80 seconds.
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