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.
.
Process data..
.
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
.
When he'as 30 secs to go, he'll've (6*400*30/400)fts to cover = 180fts
.
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
.
Give out information..
.
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.
|
|
|
