2025 AMC 10 A

Complete problem set with solutions and individual problem pages

Problem 1 Easy

Andy and Betsy both live in Mathville. Andy leaves Mathyille on his bicycle at 1:30, traveling due north at a steady 8 miles per hour. Betsy leaves on her bicycle from the same point at 2:30, traveling due east at a steady 12 miles per hour. At what time will they be exactly the same distance from their common starting point?

  • A.

    3:30

  • B.

    3:45

  • C.

    4:00

  • D.

    4:15

  • E.

    4:30

Answer:E

Let x represent Betsy's travel time in hours. Then Andy's travel time is x+1 hours. Setting up the equation based on distance traveled: 8(x+1) = 12x, which yields x = 2. Therefore, the meeting time is 4:30 PM.

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