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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
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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.

This problem has been solved

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