SOLUTION: Ryan and Nelson are in the middle of running a lap around a track. The circumference of the track is 400 feet. Ryan is 60 feet behind Nelson. Nelson is running at 6 ft/s. How fast

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Question 1094295: Ryan and Nelson are in the middle of running a lap around a track. The circumference of the track is 400 feet. Ryan is 60 feet behind Nelson. Nelson is running at 6 ft/s. How fast should Ryan run so that they both complete the lap in 30 seconds?
Found 2 solutions by Gentle Phill, ikleyn:
Answer by Gentle Phill(18)   (Show Source): You can put this solution on YOUR website!
Ryan and Nelson should be at the 400th feet together after 30 seconds.
.
Collect data..
.
Nelson running at 6ft/s is 60ft ahead of Ryan.
Ryan then runs on speed xft/s and catches up with Nelson at 400ft after 30sec.
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Process data..
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Assuming Nelson had been running on constant speed 6ft/s from start to finish, then he's going to cover the entire 400ft track in (400/6)secs
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When he'as 30 secs to go, he'll've (6*400*30/400)fts to cover = 180fts
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Nelson is 60ft behind at that time, meaning he'll've 240fts to cover
.
Equating to satisfy objective, we'll've:
.
30 seconds =
Ryan's remaining distance/his speed
= Nelson's remaining distance/his speed
.
=
.
240/x = 30
.
x = 240/30 = 8
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Give out information..
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While Nelson runs constantly at 6ft/s, Ryan should increase his speed and run at 8ft/s so that they both finish the track together within the last 30 seconds.
.
.
.
Your friend,
Francis.
Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!
.
The problem says that Ryan, who is now 60 feet behind Nelson, should catch him up in 30 seconds.


So, Ryan should running in  ft/s = 2 ft/s faster than Nelson, who runs at 6 ft/s.


Hence, Ryan' speed must be 6 + 2 = 8 ft/s.

Solved.


----------------
Nice problem.  Thanks for posting it.

If it is interesting to you,  there is a bunch  (a huge collection)  of Travel and Distance problems/lessons in this site.

They are listed in the lesson
    - OVERVIEW of lessons on Travel and Distance
from which you can easily observe them.


Actually,  all these lessons are the part of the online textbook in Algebra-I,  which I created for many years
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.


The textbook is free of charge  (as everything else in this site).

The explicit link to the textbook is
https://www.algebra.com/algebra/homework/word/travel/OVERVIEW-of-lessons-on-Travel-and-Distance.lesson


You can save this link to your archive and use it when it is needed.



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