Work through 2026 AMC 8 Problem 10 on ordering and deduction with a written solution, hints, and a visual explanation.
LogicLevel 2 · Core skill
Five runners completed the grueling Xmarathon: Luke, Melina, Nico, Olympia, and Pedro. Nico finished 11 minutes behind Pedro. Olympia finished 2 minutes ahead of Melina, but 3 minutes behind Pedro. Olympia finished 6 minutes ahead of Luke. Which runner finished fourth?
A. Luke
B. Melina
C. Nico
D. Olympia
E. Pedro
Hints
Pick one runner's time as a reference variable and express everyone else's time relative to it.
Turn each sentence into an equation using that reference variable — watch the signs for 'ahead' versus 'behind'.
Once every runner has a value in terms of the reference, sort them from smallest to largest to get the finishing order.
Read the step-by-step solution
Answer: A · Luke
Set up time differences
Let Olympia's time be O. Then Pedro = O − 3, Melina = O + 2, Luke = O + 6, and Nico = Pedro + 11 = O + 8.
Order by finish time
Pedro (O−3), Olympia (O), Melina (O+2), Luke (O+6), Nico (O+8). Luke finished fourth.