Difference between revisions of "2023 AMC 10A Problems/Problem 1"
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Cities <math>A</math> and <math>B</math> are <math>45</math> miles apart. Alicia lives in <math>A</math> and Beth lives in <math>B</math>. Alicia bikes towards <math>B</math> at 18 miles per hour. Leaving at the same time, Beth bikes toward <math>A</math> at 12 miles per hour. How many miles from City <math>A</math> will they be when they meet? | Cities <math>A</math> and <math>B</math> are <math>45</math> miles apart. Alicia lives in <math>A</math> and Beth lives in <math>B</math>. Alicia bikes towards <math>B</math> at 18 miles per hour. Leaving at the same time, Beth bikes toward <math>A</math> at 12 miles per hour. How many miles from City <math>A</math> will they be when they meet? | ||
Revision as of 15:44, 9 November 2023
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?
![\[\textbf{(A) }20\qquad\textbf{(B) }24\qquad\textbf{(C) }25\qquad\textbf{(D) }26\qquad\textbf{(E) }27\]](http://latex.artofproblemsolving.com/c/8/f/c8fdd15175bf5df101619ac5340f97dca9e75ac1.png)
Solution 1
This is a Distance=Time
Speed so let 
be the time it takes to meet. We can write the following equation:
![\[12x+18x=45\]](http://latex.artofproblemsolving.com/0/2/6/026f6ef1d38420553db4da955222cbf7eeb0952c.png)
Solving gives is 
. The 
is Alicia so 
~zhenghua
See Also
| 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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