2025 AMC 10A Problem 1

Question

Andy and Betsy both live in Mathville. Andy leaves Mathville 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?

3{:}30

3{:}45

4{:}00

4{:}15

4{:}30

Let

t

be the hours since Andy started; Andy has gone

8t

miles and Betsy

12(t-1)

miles

Set the two distances equal and solve for

t

Let

t

be the hours since

1{:}30.

Andy has gone

8t

miles north. Betsy starts an hour later, so she’s gone

12(t-1)

miles east. We want these equal:

8t = 12(t-1).

That gives

4t = 12,

so

t = 3.

Three hours past

1{:}30

is

4{:}30.

Thus, E is the correct answer.

Problem 1 in other years