2023 AMC 12A Problems/Problem 1
Contents
[hide]Problem
Cities and
are
miles apart. Alicia lives in
and Beth lives in
. Alicia bikes towards
at 18 miles per hour. Leaving at the same time, Beth bikes toward
at 12 miles per hour. How many miles from City
will they be when they meet?
Solution 1
This is a problem, so let
be the time it takes to meet. We can write the following equation:
Solving gives us
. The
is Alicia so
~zhenghua
Solution 2
The relative speed of the two is , so
hours would be required to travel
miles.
, so
~walmartbrian
Solution 3
Since mph is
times
mph, Alicia will travel
times as far as Beth. If
is the distance Beth travels,
Since this is the amount Beth traveled, the amount that Alicia traveled was
~daniel luo
See also
2023 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by First Problem |
Followed by Problem 2 |
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 AMC 12 Problems and Solutions |
2023 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by First Problem |
Followed by Problem 2 | |
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 AMC 10 Problems and Solutions |
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