Difference between revisions of "2023 AMC 8 Problems/Problem 13"
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Revision as of 09:28, 25 January 2023
Problem
Along the route of a bicycle race, 7 water stations are evenly spaced between the start and finish lines, as shown in the figure below. There are also 2 repair stations evenly spaced between the start and finish lines. The 3rd water station is located 2 miles after the 1st repair station. How long is the race in miles?
Solution
Knowing that there are 
equally spaced water stations they are each located 
, 
,… 
of the way from the start. Using the same logic for the 
station we have 
and 
for the repair stations. It is given that the 3rd water is 
miles ahead of the 
st repair station. So setting an equation we have 
getting common denominators 
so then we have 
from this.
~apex304, SohumUttamchandani, wuwang2002, TaeKim, Cxrupptedpat
Video Solution (Animated)
~Star League (https://starleague.us)
See Also
| 2023 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 12 |
Followed by Problem 14 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AJHSME/AMC 8 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
