2023 AMC 8 Problems/Problem 13
Contents
[hide]Problem
Along the route of a bicycle race, water stations are evenly spaced between the start and finish lines,
as shown in the figure below. There are also
repair stations evenly spaced between the start and
finish lines. The
rd water station is located
miles after the
st 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, MRENTHUSIASM
Video Solution (Animated)
~Star League (https://starleague.us)
Video Solution by Magic Square
https://youtu.be/-N46BeEKaCQ?t=4439
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 |
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