2021 Fall AMC 10A Problems/Problem 11
Revision as of 20:40, 22 November 2021 by Lucaszduzmatz (talk | contribs) (Created solution for 2021 AMC 10A Fall #11.)
Solution
Let the speed at which Emily walks be 42 steps per hour. Let the speed at which the ship is moving be 
. Walking in the direction of the ship, it takes her 210 steps, or 210/42 = 5 hours, to travel. We can create the equation: ![\[d = (42-s)5\]](http://latex.artofproblemsolving.com/9/1/f/91f7d7a113ae1d49423fdf4dc29d99c6ee4c7cd5.png)
Where d is the length of the ship. Walking in the opposite direction of the ship, it takes her 42 steps, or 42/42 = 1 hour. We can create a similar equation: ![\[d = (42+s)1\]](http://latex.artofproblemsolving.com/e/e/a/eea581b75a83976ed940d5e83ad0784edbae0fd0.png)
Now we have 2 variables and 2 equations, and we can solve for d.
![\[210-5s = 42 + s\]](http://latex.artofproblemsolving.com/c/f/0/cf0778c9cdf9c0cac492a7fbd4bdce382a845f81.png)
![\[s = 28\]](http://latex.artofproblemsolving.com/7/2/0/720c9cb8e094b577c9ccdcab44264da4f8189442.png)
![\[d = 42 + s = \boxed{\textbf{(A) } 70}\]](http://latex.artofproblemsolving.com/e/d/3/ed348da71c524477b4005ac8a642f2e4d47aee75.png)
~LucaszDuzMatz
