2025 AMC 10A Problems/Problem 1: Difference between revisions
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<imath>\textbf{(A) } {3:30}\qquad\textbf{(B) } {3:45}\qquad\textbf{(C) } {4:00}\qquad\textbf{(D) } {4:15}\qquad\textbf{(E) } {4:30}</imath> | <imath>\textbf{(A) } {3:30}\qquad\textbf{(B) } {3:45}\qquad\textbf{(C) } {4:00}\qquad\textbf{(D) } {4:15}\qquad\textbf{(E) } {4:30}</imath> | ||
== Solution== | == Solution 1 == | ||
We can see that Betsy travles 1 hour after Andy started. We have <imath>lcm(8, 12)=24</imath> now we can find the time traveled \(\frac{24}{8} = 3 \text{ hours}\) | We can see that Betsy travles 1 hour after Andy started. We have <imath>lcm(8, 12)=24</imath> now we can find the time traveled \(\frac{24}{8} = 3 \text{ hours}\) | ||
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-Boywithnuke(Goal: 10 followers) | -Boywithnuke(Goal: 10 followers) | ||
== Solution 2 == | |||
<imath>h</imath> hours after Betsy left, Andy has traveled <imath>8(h+1)</imath> miles, and Betsy has traveled <imath>12h</imath> miles. We are told these are equal, so <imath>8h+8=12h</imath>. Solving, we get <imath>h=2</imath>, so Andy and Betsy will be exactly the same distance from their common starting point two hours after Betsy leaves, or <imath>\text{(E) }4:30</imath>. | |||
~mithu542 | |||
Revision as of 12:47, 6 November 2025
Problem
Andy and Betsy both live in Mathville. Andy leaves Mathville on his bicycle at 
, traveling due northat a steady 
mile per hour. Betsy leaves on her bicycle from the same point at 
, traveling due east at a steady 
miles per hour. At what time will they be exactly the same distance from their common starting point?
Solution 1
We can see that Betsy travles 1 hour after Andy started. We have 
now we can find the time traveled \(\frac{24}{8} = 3 \text{ hours}\)
Now we have time \(1{:}30 + 3{:}00 = \boxed{\textbf{(E) } 4{:}30}\)
-Boywithnuke(Goal: 10 followers)
Solution 2
hours after Betsy left, Andy has traveled 
miles, and Betsy has traveled 
miles. We are told these are equal, so 
. Solving, we get 
, so Andy and Betsy will be exactly the same distance from their common starting point two hours after Betsy leaves, or 
.
~mithu542
