2025 AMC 10A Problems/Problem 1

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