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Twelve flags are evenly spaced around a running track. Ryan started running at the first flag and took 30 seconds to reach the sixth flag. How many seconds did it take Ryan, running at a constant rate, to reach the nth flag for the mth time?

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mathmate

Answer:

Ryan takes 6n+36m -42 seconds to reach the nth flag for the mth time.

Step-by-step explanation:

It takes Ryan to run from 1st to 6th flag in 30 seconds, so it takes him

30 * 6/3 = 36 seconds to make one complete round.

or it takes 6 seconds to run from one flat to the next.

To reach the nth flag (n=1,2,3,4,5, or 6)

Ryan takes 6(n-1) seconds.

To reach it the mth times, he needs to add 36(m-1) seconds.

So time it takes Ryan to reach the nth flag for the mth time takes

6(n-1) + 36(m-1)

= 6n - 6 + 36m - 36

= 6n+36m -42 seconds

Ver imagen mathmate
xero099

The time is [tex]m = 6\cdot (n-1)[/tex] seconds to reach the n-th flag.

The time needed by Ryan ([tex]t[/tex]), in seconds, to reach the n-th flag at constant velocity is modelled by the following arithmetic progression:

[tex]t = r\cdot (n-1)[/tex] (1)

Where:

  • [tex]r[/tex] - Period, in seconds per flag.
  • [tex]n[/tex] - Number of flags, in flags.

And the period can be derived from (1): ([tex]t = 30[/tex], [tex]n = 6[/tex])

[tex]r = \frac{t}{n-1}[/tex]

[tex]r = \frac{30}{6-1}[/tex]

[tex]r = 6\,\frac{s}{flag}[/tex]

If we know that [tex]n = n[/tex], [tex]t = m[/tex] and [tex]r = 6[/tex], then we have the following formula:

[tex]m = 6\cdot (n-1)[/tex]

The time is [tex]m = 6\cdot (n-1)[/tex] seconds to reach the n-th flag.

To learn more on arithmetic progressions, we kindly invite to check this verified question: https://brainly.com/question/24873057